Globular 3-cells and higher diagrams in xypic
Is there a nice/standardized way to format globular 3-cells in xypic the same way we can with 2-cells?
For 2-cells the command rtwocell generates the required arrows, and a modification that allows one to type rncell for natural numbers n would be incredible for writing category theory papers and nLab pages.
I found a page describing how to define globular 3-cells back in 2004, but xypic appears to have changed syntax signifigantly since then (or at least I am too green behind the ears to read the code there and translate it to something that works in my version of xypic). Can someone more knowledgable in LaTeX renovate these codes to work with modern xypic syntax?
Any strategy that generalizes to higher cells with arrows between arrows between arrows between... would be beautiful, but a solution for 3-cells is still greatly appreciated. Also please note that tikz solutions will be somewhat incomprehensible to me due to a lack of familiarity with the syntax, however if there is no xypic solution (and no kind samaritan willing to create one) and tikz has an elegant solution on hand I can learn some new syntax and use a tikz diagram.
After some thought I found the following solution
xymatrix{ & ddtwocell_Theta^{Theta'}{mathscr{M}} \ A ar@/^5.5pc/[rr]^F ar@/_5.5pc/[rr]_G & & B \ & }
which generates the diagram below
and it's relatively straightforward (but time consuming) to switch inner arrow directions and generalize further, but this still has uniform arrow types instead of increasing degrees of 'hollowness' as in the first diagram above, so a solution that can accommodate for this would be appreciated.
diagrams xy-pic
asked 55 mins ago
Alec RheaAlec Rhea
1205
add a comment |
Is there a nice/standardized way to format globular 3-cells in xypic the same way we can with 2-cells?
For 2-cells the command rtwocell generates the required arrows, and a modification that allows one to type rncell for natural numbers n would be incredible for writing category theory papers and nLab pages.
I found a page describing how to define globular 3-cells back in 2004, but xypic appears to have changed syntax signifigantly since then (or at least I am too green behind the ears to read the code there and translate it to something that works in my version of xypic). Can someone more knowledgable in LaTeX renovate these codes to work with modern xypic syntax?
Any strategy that generalizes to higher cells with arrows between arrows between arrows between... would be beautiful, but a solution for 3-cells is still greatly appreciated. Also please note that tikz solutions will be somewhat incomprehensible to me due to a lack of familiarity with the syntax, however if there is no xypic solution (and no kind samaritan willing to create one) and tikz has an elegant solution on hand I can learn some new syntax and use a tikz diagram.
After some thought I found the following solution
xymatrix{ & ddtwocell_Theta^{Theta'}{mathscr{M}} \ A ar@/^5.5pc/[rr]^F ar@/_5.5pc/[rr]_G & & B \ & }
which generates the diagram below
and it's relatively straightforward (but time consuming) to switch inner arrow directions and generalize further, but this still has uniform arrow types instead of increasing degrees of 'hollowness' as in the first diagram above, so a solution that can accommodate for this would be appreciated.
diagrams xy-pic
asked 55 mins ago
Alec RheaAlec Rhea
1205
add a comment |
Is there a nice/standardized way to format globular 3-cells in xypic the same way we can with 2-cells?
For 2-cells the command rtwocell generates the required arrows, and a modification that allows one to type rncell for natural numbers n would be incredible for writing category theory papers and nLab pages.
I found a page describing how to define globular 3-cells back in 2004, but xypic appears to have changed syntax signifigantly since then (or at least I am too green behind the ears to read the code there and translate it to something that works in my version of xypic). Can someone more knowledgable in LaTeX renovate these codes to work with modern xypic syntax?
Any strategy that generalizes to higher cells with arrows between arrows between arrows between... would be beautiful, but a solution for 3-cells is still greatly appreciated. Also please note that tikz solutions will be somewhat incomprehensible to me due to a lack of familiarity with the syntax, however if there is no xypic solution (and no kind samaritan willing to create one) and tikz has an elegant solution on hand I can learn some new syntax and use a tikz diagram.
After some thought I found the following solution
xymatrix{ & ddtwocell_Theta^{Theta'}{mathscr{M}} \ A ar@/^5.5pc/[rr]^F ar@/_5.5pc/[rr]_G & & B \ & }
which generates the diagram below
and it's relatively straightforward (but time consuming) to switch inner arrow directions and generalize further, but this still has uniform arrow types instead of increasing degrees of 'hollowness' as in the first diagram above, so a solution that can accommodate for this would be appreciated.
diagrams xy-pic
asked 55 mins ago
Alec RheaAlec Rhea
1205
Is there a nice/standardized way to format globular 3-cells in xypic the same way we can with 2-cells?
For 2-cells the command rtwocell generates the required arrows, and a modification that allows one to type rncell for natural numbers n would be incredible for writing category theory papers and nLab pages.
I found a page describing how to define globular 3-cells back in 2004, but xypic appears to have changed syntax signifigantly since then (or at least I am too green behind the ears to read the code there and translate it to something that works in my version of xypic). Can someone more knowledgable in LaTeX renovate these codes to work with modern xypic syntax?
Any strategy that generalizes to higher cells with arrows between arrows between arrows between... would be beautiful, but a solution for 3-cells is still greatly appreciated. Also please note that tikz solutions will be somewhat incomprehensible to me due to a lack of familiarity with the syntax, however if there is no xypic solution (and no kind samaritan willing to create one) and tikz has an elegant solution on hand I can learn some new syntax and use a tikz diagram.
After some thought I found the following solution
xymatrix{ & ddtwocell_Theta^{Theta'}{mathscr{M}} \ A ar@/^5.5pc/[rr]^F ar@/_5.5pc/[rr]_G & & B \ & }
which generates the diagram below
and it's relatively straightforward (but time consuming) to switch inner arrow directions and generalize further, but this still has uniform arrow types instead of increasing degrees of 'hollowness' as in the first diagram above, so a solution that can accommodate for this would be appreciated.
diagrams xy-pic
diagrams xy-pic
asked 55 mins ago
Alec RheaAlec Rhea
1205
asked 55 mins ago
Alec RheaAlec Rhea
1205
edited 18 mins ago
Alec Rhea
asked 55 mins ago
Alec RheaAlec Rhea
1205
asked 55 mins ago
Alec RheaAlec Rhea
1205
asked 55 mins ago
Alec RheaAlec Rhea
1205
1205
add a comment |
add a comment |
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