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Nov
22
asked Why are there no naturality condition in definition of exponential in a category?
Nov
22
comment Category theory - where is my error?
When $p$ is a vertex (that is a function) it is clear. But $p$ may also be an edge and an edge is not a function. I don't understand this
Nov
21
accepted Category theory - where is my error?
Nov
21
comment Category theory - where is my error?
Yes, I confused the set $\operatorname{MOR}(A;B)$ itself with elements of this set. Thanks for explaining, I will upvote your answer
Nov
21
comment Category theory - where is my error?
@GiorgioMossa: It isn't the category of graphs. It is the category of (discretely) continuous maps between digraphs. Objects are digraphs not vertexes and edges
Nov
21
comment Category theory - where is my error?
Again no: objects of category $\mathbf{Dig}$ are digraphs. $p$ and $q$ are objects that is digraphs, not vertexes or edges.
Nov
21
comment Category theory - where is my error?
By $\operatorname{MOR}(A;B)$ I mean the internal morphisms (=categorical exponentials) from $A$ to $B$. Internal morphisms are objects (digraphs in our case)
Nov
21
comment Category theory - where is my error?
@GiorgioMossa: $\epsilon(p;q)$ is $\epsilon$ function applied to the ordered pair $(p;q)$ of digraphs. $1_{MOR(A;B)}(p)(q)$ means the result of $1_{MOR(A;B)}(p)$ applied to the digraph $q$.
Nov
21
asked Category theory - where is my error?
Nov
18
comment Explicit formula for exponential objects in category of digraphs
Could you indeed provide explicit formulas for evaluation and transpose? It seems that I misunderstand something, I can't get the formulas to coincide
Nov
17
comment Is a set closed under finite intersections? (about filters)
It is enough to prove that for every $f \in \operatorname{GR} ( \Delta \times^{\mathsf{FCD}} \Delta)$ there is a positive $\varepsilon$ such that $\forall x \in ( - \varepsilon ; \varepsilon) : f[\{x\}] \in \Delta$.
Nov
17
accepted Explicit formula for exponential objects in category of digraphs
Nov
17
comment Explicit formula for exponential objects in category of digraphs
That you for your answer. However explicit formulas for evaluation and transpose (and proof that they are really evaluation and transpose) are missing.
Nov
16
revised Explicit formula for exponential objects in category of digraphs
added 26 characters in body
Nov
16
comment Explicit formula for exponential objects in category of digraphs
That category $\mathbf{Dig}$ has products follows from my draft article mathematics21.org/binaries/product.pdf
Nov
16
asked Explicit formula for exponential objects in category of digraphs
Nov
16
accepted Neighborhood of diagonal
Nov
16
accepted A function continuous in both arguments
Nov
16
accepted “Uniform groups” (similar to topological groups)?
Nov
16
accepted Double embedding or double restriction