Diagram of Short exact sequences












0














Can someone help me. I want to write morphisms between all objects



[

  setlength{arraycolsep}{1pt}

  begin{array}{*{9}c}

    0 &Lrightarrow & X & Lrightarrow & Y & Lrightarrow & Z & Lrightarrow & 0\

    & & Ldownarrow & & Ldownarrow & & Ldownarrow & & \

    0 &Lrightarrow & X^' & Lrightarrow & Y^' & Lrightarrow & Z^' &  Lrightarrow & 0

  end{array}

]





commutative-diagrams







share|improve this question









New contributor




Diego Havez is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
















  • 1




    Sorry, what has your question to do with tikz-pgf? And please consider providing a compilable code.
    – marmot
    2 hours ago










  • What are Lrightarrow and Ldownarrow?
    – Bernard
    2 hours ago










  • It is compilable in my latex. Do you have another code from titkz-pgf?
    – Diego Havez
    2 hours ago










  • Bernard to be honest, I do not know, I just need to write morphisms between objects.
    – Diego Havez
    2 hours ago
















0














Can someone help me. I want to write morphisms between all objects



[

  setlength{arraycolsep}{1pt}

  begin{array}{*{9}c}

    0 &Lrightarrow & X & Lrightarrow & Y & Lrightarrow & Z & Lrightarrow & 0\

    & & Ldownarrow & & Ldownarrow & & Ldownarrow & & \

    0 &Lrightarrow & X^' & Lrightarrow & Y^' & Lrightarrow & Z^' &  Lrightarrow & 0

  end{array}

]





commutative-diagrams







share|improve this question









New contributor




Diego Havez is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
















  • 1




    Sorry, what has your question to do with tikz-pgf? And please consider providing a compilable code.
    – marmot
    2 hours ago










  • What are Lrightarrow and Ldownarrow?
    – Bernard
    2 hours ago










  • It is compilable in my latex. Do you have another code from titkz-pgf?
    – Diego Havez
    2 hours ago










  • Bernard to be honest, I do not know, I just need to write morphisms between objects.
    – Diego Havez
    2 hours ago














0












0








0







Can someone help me. I want to write morphisms between all objects



[

  setlength{arraycolsep}{1pt}

  begin{array}{*{9}c}

    0 &Lrightarrow & X & Lrightarrow & Y & Lrightarrow & Z & Lrightarrow & 0\

    & & Ldownarrow & & Ldownarrow & & Ldownarrow & & \

    0 &Lrightarrow & X^' & Lrightarrow & Y^' & Lrightarrow & Z^' &  Lrightarrow & 0

  end{array}

]





commutative-diagrams







share|improve this question









New contributor




Diego Havez is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











Can someone help me. I want to write morphisms between all objects



[

  setlength{arraycolsep}{1pt}

  begin{array}{*{9}c}

    0 &Lrightarrow & X & Lrightarrow & Y & Lrightarrow & Z & Lrightarrow & 0\

    & & Ldownarrow & & Ldownarrow & & Ldownarrow & & \

    0 &Lrightarrow & X^' & Lrightarrow & Y^' & Lrightarrow & Z^' &  Lrightarrow & 0

  end{array}

]





commutative-diagrams




commutative-diagrams






share|improve this question









New contributor




Diego Havez is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|improve this question









New contributor




Diego Havez is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|improve this question




share|improve this question








edited 2 hours ago









Sigur

24.3k355137




24.3k355137






New contributor




Diego Havez is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









asked 2 hours ago









Diego HavezDiego Havez

212




212




New contributor




Diego Havez is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





Diego Havez is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Diego Havez is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.








  • 1




    Sorry, what has your question to do with tikz-pgf? And please consider providing a compilable code.
    – marmot
    2 hours ago










  • What are Lrightarrow and Ldownarrow?
    – Bernard
    2 hours ago










  • It is compilable in my latex. Do you have another code from titkz-pgf?
    – Diego Havez
    2 hours ago










  • Bernard to be honest, I do not know, I just need to write morphisms between objects.
    – Diego Havez
    2 hours ago














  • 1




    Sorry, what has your question to do with tikz-pgf? And please consider providing a compilable code.
    – marmot
    2 hours ago










  • What are Lrightarrow and Ldownarrow?
    – Bernard
    2 hours ago










  • It is compilable in my latex. Do you have another code from titkz-pgf?
    – Diego Havez
    2 hours ago










  • Bernard to be honest, I do not know, I just need to write morphisms between objects.
    – Diego Havez
    2 hours ago








1




1




Sorry, what has your question to do with tikz-pgf? And please consider providing a compilable code.
– marmot
2 hours ago




Sorry, what has your question to do with tikz-pgf? And please consider providing a compilable code.
– marmot
2 hours ago












What are Lrightarrow and Ldownarrow?
– Bernard
2 hours ago




What are Lrightarrow and Ldownarrow?
– Bernard
2 hours ago












It is compilable in my latex. Do you have another code from titkz-pgf?
– Diego Havez
2 hours ago




It is compilable in my latex. Do you have another code from titkz-pgf?
– Diego Havez
2 hours ago












Bernard to be honest, I do not know, I just need to write morphisms between objects.
– Diego Havez
2 hours ago




Bernard to be honest, I do not know, I just need to write morphisms between objects.
– Diego Havez
2 hours ago










2 Answers
2






active

oldest

votes


















2














Here are solutions with xy and tikz-cd. The idea is the same, think on them as matrices.



enter image description here



documentclass{report}

usepackage[all]{xy}

usepackage{tikz-cd}

begin{document}

[

xymatrix{

  0 ar[r] & A ar[d]_-{alpha} ar[r]^-{f} & B ar[d]_-{beta} ar[r]^-{g} & C ar[d]^-{gamma} ar[r] & 0 \

  0 ar[r] & A' ar[r]_-{f'} & B' ar[r]_-{g'} & C' ar[r] & 0

}

]

[

begin{tikzcd}

  0 arrow[r] & A arrow[d, "alpha"] arrow[r, "f"] & B arrow[d, "beta"] arrow[r, "g"] & C arrow[d, "gamma"] arrow[r] & 0 \

  0 arrow[r] & A' arrow[r, "f'"] & B' arrow[r, "g'"] & C' ar[r] & 0

end{tikzcd}

]

end{document}





share|improve this answer























  • Sigur thank you very much.
    – Diego Havez
    2 hours ago










  • @DiegoHavez, welcome.
    – Sigur
    2 hours ago



















1














A solution with psmatrix:



documentclass{article}



usepackage{pst-node}

usepackage{auto-pst-pdf} 



begin{document}



   [

everypsbox{scriptstyle}

    begin{psmatrix}[rowsep=1cm, colsep=1.2cm]

    0 & A & B & C & 0 \

    0 & D & B' & C' & 0

    %% Arrows

    psset{linewidth=0.5pt, arrows=->, arrowinset=0.12, nodesep=3pt, shortput=nab, labelsep=1.5pt}

    ncline{1,1}{1,2}ncline{1,4}{1,5}ncline{2,1}{2,2}ncline{2,4}{2,5}

    ncline{1,2}{1,3}^{f}ncline{1,2}{2,2}_{alpha}

    ncline{1,3}{1,4}^{g}ncline{1,3}{2,3}_{beta}ncline{1,4}{2,4}_{gamma}

    ncline{2,2}{2,3}_{f'}

    ncline{2,3}{2,4}_{g'}

   end{psmatrix} ]%



end{document}


enter image description here






share|improve this answer





















  • Do you know the meaning of nc in ncline command? I mean, line is clear; c maybe for column; and what about n?
    – Sigur
    1 hour ago






  • 1




    nc is for node connection, as far as I know.
    – Bernard
    1 hour ago










  • ahh, makes sense. Nice!
    – Sigur
    1 hour ago











Your Answer








StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "85"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});

function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});


}
});






Diego Havez is a new contributor. Be nice, and check out our Code of Conduct.










draft saved

draft discarded


















StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2ftex.stackexchange.com%2fquestions%2f469450%2fdiagram-of-short-exact-sequences%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown

























2 Answers
2






active

oldest

votes








2 Answers
2






active

oldest

votes









active

oldest

votes






active

oldest

votes









2














Here are solutions with xy and tikz-cd. The idea is the same, think on them as matrices.



enter image description here



documentclass{report}

usepackage[all]{xy}

usepackage{tikz-cd}

begin{document}

[

xymatrix{

  0 ar[r] & A ar[d]_-{alpha} ar[r]^-{f} & B ar[d]_-{beta} ar[r]^-{g} & C ar[d]^-{gamma} ar[r] & 0 \

  0 ar[r] & A' ar[r]_-{f'} & B' ar[r]_-{g'} & C' ar[r] & 0

}

]

[

begin{tikzcd}

  0 arrow[r] & A arrow[d, "alpha"] arrow[r, "f"] & B arrow[d, "beta"] arrow[r, "g"] & C arrow[d, "gamma"] arrow[r] & 0 \

  0 arrow[r] & A' arrow[r, "f'"] & B' arrow[r, "g'"] & C' ar[r] & 0

end{tikzcd}

]

end{document}





share|improve this answer























  • Sigur thank you very much.
    – Diego Havez
    2 hours ago










  • @DiegoHavez, welcome.
    – Sigur
    2 hours ago
















2














Here are solutions with xy and tikz-cd. The idea is the same, think on them as matrices.



enter image description here



documentclass{report}

usepackage[all]{xy}

usepackage{tikz-cd}

begin{document}

[

xymatrix{

  0 ar[r] & A ar[d]_-{alpha} ar[r]^-{f} & B ar[d]_-{beta} ar[r]^-{g} & C ar[d]^-{gamma} ar[r] & 0 \

  0 ar[r] & A' ar[r]_-{f'} & B' ar[r]_-{g'} & C' ar[r] & 0

}

]

[

begin{tikzcd}

  0 arrow[r] & A arrow[d, "alpha"] arrow[r, "f"] & B arrow[d, "beta"] arrow[r, "g"] & C arrow[d, "gamma"] arrow[r] & 0 \

  0 arrow[r] & A' arrow[r, "f'"] & B' arrow[r, "g'"] & C' ar[r] & 0

end{tikzcd}

]

end{document}





share|improve this answer























  • Sigur thank you very much.
    – Diego Havez
    2 hours ago










  • @DiegoHavez, welcome.
    – Sigur
    2 hours ago














2












2








2






Here are solutions with xy and tikz-cd. The idea is the same, think on them as matrices.



enter image description here



documentclass{report}

usepackage[all]{xy}

usepackage{tikz-cd}

begin{document}

[

xymatrix{

  0 ar[r] & A ar[d]_-{alpha} ar[r]^-{f} & B ar[d]_-{beta} ar[r]^-{g} & C ar[d]^-{gamma} ar[r] & 0 \

  0 ar[r] & A' ar[r]_-{f'} & B' ar[r]_-{g'} & C' ar[r] & 0

}

]

[

begin{tikzcd}

  0 arrow[r] & A arrow[d, "alpha"] arrow[r, "f"] & B arrow[d, "beta"] arrow[r, "g"] & C arrow[d, "gamma"] arrow[r] & 0 \

  0 arrow[r] & A' arrow[r, "f'"] & B' arrow[r, "g'"] & C' ar[r] & 0

end{tikzcd}

]

end{document}





share|improve this answer














Here are solutions with xy and tikz-cd. The idea is the same, think on them as matrices.



enter image description here



documentclass{report}

usepackage[all]{xy}

usepackage{tikz-cd}

begin{document}

[

xymatrix{

  0 ar[r] & A ar[d]_-{alpha} ar[r]^-{f} & B ar[d]_-{beta} ar[r]^-{g} & C ar[d]^-{gamma} ar[r] & 0 \

  0 ar[r] & A' ar[r]_-{f'} & B' ar[r]_-{g'} & C' ar[r] & 0

}

]

[

begin{tikzcd}

  0 arrow[r] & A arrow[d, "alpha"] arrow[r, "f"] & B arrow[d, "beta"] arrow[r, "g"] & C arrow[d, "gamma"] arrow[r] & 0 \

  0 arrow[r] & A' arrow[r, "f'"] & B' arrow[r, "g'"] & C' ar[r] & 0

end{tikzcd}

]

end{document}






share|improve this answer














share|improve this answer



share|improve this answer








edited 2 hours ago

























answered 2 hours ago









SigurSigur

24.3k355137




24.3k355137












  • Sigur thank you very much.
    – Diego Havez
    2 hours ago










  • @DiegoHavez, welcome.
    – Sigur
    2 hours ago


















  • Sigur thank you very much.
    – Diego Havez
    2 hours ago










  • @DiegoHavez, welcome.
    – Sigur
    2 hours ago
















Sigur thank you very much.
– Diego Havez
2 hours ago




Sigur thank you very much.
– Diego Havez
2 hours ago












@DiegoHavez, welcome.
– Sigur
2 hours ago




@DiegoHavez, welcome.
– Sigur
2 hours ago











1














A solution with psmatrix:



documentclass{article}



usepackage{pst-node}

usepackage{auto-pst-pdf} 



begin{document}



   [

everypsbox{scriptstyle}

    begin{psmatrix}[rowsep=1cm, colsep=1.2cm]

    0 & A & B & C & 0 \

    0 & D & B' & C' & 0

    %% Arrows

    psset{linewidth=0.5pt, arrows=->, arrowinset=0.12, nodesep=3pt, shortput=nab, labelsep=1.5pt}

    ncline{1,1}{1,2}ncline{1,4}{1,5}ncline{2,1}{2,2}ncline{2,4}{2,5}

    ncline{1,2}{1,3}^{f}ncline{1,2}{2,2}_{alpha}

    ncline{1,3}{1,4}^{g}ncline{1,3}{2,3}_{beta}ncline{1,4}{2,4}_{gamma}

    ncline{2,2}{2,3}_{f'}

    ncline{2,3}{2,4}_{g'}

   end{psmatrix} ]%



end{document}


enter image description here






share|improve this answer





















  • Do you know the meaning of nc in ncline command? I mean, line is clear; c maybe for column; and what about n?
    – Sigur
    1 hour ago






  • 1




    nc is for node connection, as far as I know.
    – Bernard
    1 hour ago










  • ahh, makes sense. Nice!
    – Sigur
    1 hour ago
















1














A solution with psmatrix:



documentclass{article}



usepackage{pst-node}

usepackage{auto-pst-pdf} 



begin{document}



   [

everypsbox{scriptstyle}

    begin{psmatrix}[rowsep=1cm, colsep=1.2cm]

    0 & A & B & C & 0 \

    0 & D & B' & C' & 0

    %% Arrows

    psset{linewidth=0.5pt, arrows=->, arrowinset=0.12, nodesep=3pt, shortput=nab, labelsep=1.5pt}

    ncline{1,1}{1,2}ncline{1,4}{1,5}ncline{2,1}{2,2}ncline{2,4}{2,5}

    ncline{1,2}{1,3}^{f}ncline{1,2}{2,2}_{alpha}

    ncline{1,3}{1,4}^{g}ncline{1,3}{2,3}_{beta}ncline{1,4}{2,4}_{gamma}

    ncline{2,2}{2,3}_{f'}

    ncline{2,3}{2,4}_{g'}

   end{psmatrix} ]%



end{document}


enter image description here






share|improve this answer





















  • Do you know the meaning of nc in ncline command? I mean, line is clear; c maybe for column; and what about n?
    – Sigur
    1 hour ago






  • 1




    nc is for node connection, as far as I know.
    – Bernard
    1 hour ago










  • ahh, makes sense. Nice!
    – Sigur
    1 hour ago














1












1








1






A solution with psmatrix:



documentclass{article}



usepackage{pst-node}

usepackage{auto-pst-pdf} 



begin{document}



   [

everypsbox{scriptstyle}

    begin{psmatrix}[rowsep=1cm, colsep=1.2cm]

    0 & A & B & C & 0 \

    0 & D & B' & C' & 0

    %% Arrows

    psset{linewidth=0.5pt, arrows=->, arrowinset=0.12, nodesep=3pt, shortput=nab, labelsep=1.5pt}

    ncline{1,1}{1,2}ncline{1,4}{1,5}ncline{2,1}{2,2}ncline{2,4}{2,5}

    ncline{1,2}{1,3}^{f}ncline{1,2}{2,2}_{alpha}

    ncline{1,3}{1,4}^{g}ncline{1,3}{2,3}_{beta}ncline{1,4}{2,4}_{gamma}

    ncline{2,2}{2,3}_{f'}

    ncline{2,3}{2,4}_{g'}

   end{psmatrix} ]%



end{document}


enter image description here






share|improve this answer












A solution with psmatrix:



documentclass{article}



usepackage{pst-node}

usepackage{auto-pst-pdf} 



begin{document}



   [

everypsbox{scriptstyle}

    begin{psmatrix}[rowsep=1cm, colsep=1.2cm]

    0 & A & B & C & 0 \

    0 & D & B' & C' & 0

    %% Arrows

    psset{linewidth=0.5pt, arrows=->, arrowinset=0.12, nodesep=3pt, shortput=nab, labelsep=1.5pt}

    ncline{1,1}{1,2}ncline{1,4}{1,5}ncline{2,1}{2,2}ncline{2,4}{2,5}

    ncline{1,2}{1,3}^{f}ncline{1,2}{2,2}_{alpha}

    ncline{1,3}{1,4}^{g}ncline{1,3}{2,3}_{beta}ncline{1,4}{2,4}_{gamma}

    ncline{2,2}{2,3}_{f'}

    ncline{2,3}{2,4}_{g'}

   end{psmatrix} ]%



end{document}


enter image description here







share|improve this answer












share|improve this answer



share|improve this answer










answered 1 hour ago









BernardBernard

166k769194




166k769194












  • Do you know the meaning of nc in ncline command? I mean, line is clear; c maybe for column; and what about n?
    – Sigur
    1 hour ago






  • 1




    nc is for node connection, as far as I know.
    – Bernard
    1 hour ago










  • ahh, makes sense. Nice!
    – Sigur
    1 hour ago


















  • Do you know the meaning of nc in ncline command? I mean, line is clear; c maybe for column; and what about n?
    – Sigur
    1 hour ago






  • 1




    nc is for node connection, as far as I know.
    – Bernard
    1 hour ago










  • ahh, makes sense. Nice!
    – Sigur
    1 hour ago
















Do you know the meaning of nc in ncline command? I mean, line is clear; c maybe for column; and what about n?
– Sigur
1 hour ago




Do you know the meaning of nc in ncline command? I mean, line is clear; c maybe for column; and what about n?
– Sigur
1 hour ago




1




1




nc is for node connection, as far as I know.
– Bernard
1 hour ago




nc is for node connection, as far as I know.
– Bernard
1 hour ago












ahh, makes sense. Nice!
– Sigur
1 hour ago




ahh, makes sense. Nice!
– Sigur
1 hour ago










Diego Havez is a new contributor. Be nice, and check out our Code of Conduct.










draft saved

draft discarded


















Diego Havez is a new contributor. Be nice, and check out our Code of Conduct.













Diego Havez is a new contributor. Be nice, and check out our Code of Conduct.












Diego Havez is a new contributor. Be nice, and check out our Code of Conduct.
















Thanks for contributing an answer to TeX - LaTeX Stack Exchange!


  • Please be sure to answer the question. Provide details and share your research!

But avoid …



  • Asking for help, clarification, or responding to other answers.

  • Making statements based on opinion; back them up with references or personal experience.


To learn more, see our tips on writing great answers.





Some of your past answers have not been well-received, and you're in danger of being blocked from answering.


Please pay close attention to the following guidance:


  • Please be sure to answer the question. Provide details and share your research!

But avoid …



  • Asking for help, clarification, or responding to other answers.

  • Making statements based on opinion; back them up with references or personal experience.


To learn more, see our tips on writing great answers.




draft saved


draft discarded














StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2ftex.stackexchange.com%2fquestions%2f469450%2fdiagram-of-short-exact-sequences%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown





















































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown

































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown







-

Popular posts from this blog

Lallio

Image
Coordenadas: 45° 40' N 9° 38' E Lallio      Comuna    Lallio Localização de Lallio na Itália Coordenadas 45° 40' N 9° 38' E Região Lombardia Província Bérgamo Área - Total 2 km² Altitude 216 m População  - Total 3 826     • Densidade 1 913 hab./km² Outros dados Comunas limítrofes Bergamo, Dalmine, Stezzano, Treviolo Código ISTAT 016123 Código cadastral E422 Código postal 24040 Prefixo telefônico 035 Website www.comune.lallio.bg.it Lallio é uma comuna italiana da região da Lombardia, província de Bérgamo, com cerca de 3.826 habitantes. Estende-se por uma área de 2 km², tendo uma densidade populacional de 1913 hab/km². Faz fronteira com Bergamo, Dalmine, Stezzano, Treviolo. [ 1 ] [ 2 ] [ 3 ] Demografia | Variação demográfica do município entre 1861 e 2011 [ 3 ] Fonte : Istituto Nazionale di Statistica (ISTAT) - Elabor...
Read more

Unable to find Lightning Node

Image
2 I have successfully installed and synced my lightning node (Raspiblitz). I see my public ip on port 8333 has 8 conns. However, when I check my node on 1ml.com my node is not found. I did forward port 8333 and 9735 on my router. Should I connect to a peer or create a channel before my node is visible for the outside? lightning-network lightning-network-daemon share | improve this question asked 1 hour ago Bart DV Bart DV 31 3 add a comment  |  ...
Read more

Futebolista

Image
Ronaldo primeiro jogador a ser eleito por três vezes o melhor jogador do mundo pela FIFA. Ronaldinho Gaúcho atuando pelo Barcelona onde foi duas vezes eleito o melhor jogador do mundo pela FIFA. Kaká atuando pelo Milan onde foi eleito em 2007 o melhor jogador do mundo pela FIFA. Lothar Matthäus primeiro jogador a ser eleito o melhor jogador do mundo pela FIFA em 1991 pela Inter de Milão. Neymar durante partida contra a Escócia, em 27 de março de 2011. Crianças praticando futebol. Robinho, futebolista brasileiro, em 15 de novembro de 2006. Atletas do Chelsea, da Inglaterra. A venda de camisas com nome e número dos jogadores é uma grande fonte de arrecadação. Jürgen Klinsmann atuou como jogador e foi treinador da Alemanha. Estádio de futebol, principal local onde laboram os jogadores. O jogador de futebol , ou Futebolista , é um atleta profissional de futebol, e cuja prática do desporto coletivo é fundamental. Estes trabalhadores sã...
Read more