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Aug
27
accepted An endomorphism $f$ such that $f\circ f=1$
Aug
6
comment Notation about commutative diagrams and their vertices
@RobArthan But I need to explicitly refer to different vertices in my proof text. Well, maybe I should just say like "top right" node of the square diagram?
Aug
6
comment Notation about commutative diagrams and their vertices
Well, what's about $0[A]\overset{f}{\leftrightarrow} 1[A]$ or $A[0]\overset{f}{\leftrightarrow} A[1]$?
Aug
6
asked Notation about commutative diagrams and their vertices
Aug
5
comment Help to write a proof (category theory diagram)
What about the similar question for a square graph?
Aug
5
comment Help to write a proof (category theory diagram)
@PVAL Also this proves only that cycles are identities, but we need to prove also that the diagram is commutative
Aug
5
comment Help to write a proof (category theory diagram)
@PVAL But how to show that every cycle is composed from cycles of the length no more than 3?
Aug
5
comment How do we prove commutativity of a diagram?
@RobArthan I haven't asked whether "a technique for dealing with the infinite" exists. I ask about a particular technique tailored with category theory diagrams, which I can use to prove particular results for a specific diagram
Aug
5
asked Help to write a proof (category theory diagram)
Aug
5
comment How do we prove commutativity of a diagram?
Isn't referring to a particular diagram as planar "proof by a picture"? How to show that a diagram is planar without writing actual X-Y equations of the curves which serve as graph edges?
Aug
5
accepted Every cycle is a composition of simple cycles
Aug
5
comment How do we prove commutativity of a diagram?
@DanielFischer What is "cell"? Why is this enough?
Aug
5
asked How do we prove commutativity of a diagram?
Aug
1
revised Every cycle is a composition of simple cycles
finite
Aug
1
asked Every cycle is a composition of simple cycles
Jul
25
accepted Two “adjunct” (quasi-inverse) functions
Jul
23
revised Two “adjunct” (quasi-inverse) functions
clarification
Jul
23
revised Two “adjunct” (quasi-inverse) functions
additional condition for $p$ and $q$.
Jul
23
answered Two “adjunct” (quasi-inverse) functions
Jul
23
asked Two “adjunct” (quasi-inverse) functions