yogsototh/categories
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

testing

Browse source
This commit is contained in:
Yann Esposito 2012-10-12 17:11:55 +02:00
parent d328927e89
commit 0b244e6615
1 changed files with 21 additions and 9 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

30
00_Introduction.lhs
View file

@ -81,9 +81,9 @@ A -> B [label="f∘idA=f=idB∘f"]
A -> B [label="f"]
B -> C [label="g"]
C -> D [label="h"]
A -> C [label="g∘f",style="bold",fontcolor="cyan",color="cyan"]
B -> D [label="h∘g",style="bold",fontcolor="yellow",color="yellow"]
A -> D [label="(h∘g)∘f=h∘(g∘f)",style="bold",color="red",fontcolor="red"]
A -> C [label="g∘f",style="bold",fontcolor="cyan",color="cyan",constraint="false"]
B -> D [label="h∘g",style="bold",fontcolor="yellow",color="yellow",constraint="false"]
A -> D [label="(h∘g)∘f=h∘(g∘f)",style="bold",color="red",fontcolor="red",constraint="false"]
</graph>
### Representation of Category
@ -124,17 +124,21 @@ We simply add a relation between 3 arrows that represent the composition.
<graph title="Naïve Category Representation">
f[label="", fixedsize="false", width=0,height=0,shape=none];
A[pos="0,0!"]
B[pos="1.5,1.5!"]
C[pos="3,0!"]
f[pos="0.75,0.75!",label="", fixedsize="false", width=0,height=0,shape=none];
A -> f[label="f", arrowhead=None]
f -> B
g[label="", fixedsize="false", width=0,height=0,shape=none];
g[pos="2.25,0.75!",label="", fixedsize="false", width=0,height=0,shape=none];
B -> g[label="g", arrowhead=None]
g -> C
fg [label="", fixedsize="false", width=0,height=0,shape=none];
AC [label="", fixedsize="false", width=0,height=0,shape=none];
fg [pos="1.5,0.75!",label="", fixedsize="false", width=0,height=0,shape=none];
AC [pos="1.5,0!",label="", fixedsize="false", width=0,height=0,shape=none];
f -> fg [color="red",style=dashed,arrowhead=None]
fg -> g [color="red",style=dashed,arrowhead=None]
@ -233,7 +237,7 @@ B -> C
A -> C [constraint=false]
</graph>
<graph title="Not a category; think about \(g∘f\).">
<graph title="Cannot be a category; no candidate for \(g∘f\).">
A[label="★"]
B[label="★"]
C[label="★"]
@ -261,7 +265,7 @@ B -> A
C -> A
</graph>
<graph title="Not a category; \((h∘g)∘f=idB∘f=f≠h=h∘idA=h∘(g∘f)\)">
<graph title="Cannot be a category ; no possible associative ∘<br/>\((h∘g)∘f=idB∘f=f≠h=h∘idA=h∘(g∘f)\)">
A -> B[label="g"]
B -> A[label="f"]
B -> A[label="h"]
@ -309,3 +313,11 @@ Typical examples:
★ -> ★[label="..."]
</graph>
metapost test
<mpost title="metapost test">
pair A, B, C;
A:=(0,0); B:=(1cm,0); C:=(0,1cm);
draw A--B--C;
</mpost>