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RandomGraph[{10,20},DirectedEdgesTrue]
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TransitiveClosureGraph
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Graph[Join[EdgeList[%],##&/@VertexList[%]]]
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LayeredGraphPlot[%]
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RandomGraph[{3,5},DirectedEdgesTrue,VertexLabelsAutomatic,EdgeLabels"Name"]
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RandomGraph[{4,5},DirectedEdgesTrue,VertexLabelsAutomatic,EdgeLabels"Name"]
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PathGraph[Range[4],DirectedEdgesTrue,VertexLabelsAutomatic]
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PathGraph[Range[5],DirectedEdgesTrue,VertexLabelsAutomatic]
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Category of graphs...
graph cat
int,list
list[int]
list[list[int]]
f[int]int(*type:intint*)
g[int]list[int]
morphisms :
identity morphism :
f[int]int
g[f[int]]:intintlist[int]
int int
set set
set of morphisms between objects ; can you represent that set as itself a member of the category (-> closed category)
expr
f[g[x_],y_]h[x,y]
closed categories programs=data
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AxiomaticTheory["GroupAxioms"]
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{a.,b.,c.}
a.(b.c.)(a.b.)c.,
a.
a.
1
a.,
a.
a.
a.
1
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CayleyGraph[AlternatingGroup[4]]
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TransitiveClosureGraph[%]
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sieve
Lawvere-Tierney
state vertex is like an open set
λ a λ b .
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