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