Questions tagged [protomodular-categories]

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Names for $\operatorname{Coker}\operatorname{ker}\cong \operatorname{Ker}\operatorname{coker}$ and $\operatorname{Coim}\cong \operatorname{Im}$?

Let $\operatorname{Coim}f$ be the cokernel of the kernel pair of an arrow. Let $\operatorname{Im}f$ be the kernel of the cokernel pair. An interesting property of a category is the isomorphy of the ...
4
votes
0answers
162 views

Relationship between pointed protomodularity and $\operatorname{Coker}\ker f\overset{\cong}{\longrightarrow}\operatorname{Ker}\operatorname{coker}f$

In hopes of understanding algebra better, I've been reading here and there about protomodular categories and the like. Among other things, the theory surrounding these (and some other) categories ...
2
votes
1answer
150 views

Why does the monoid of central morphisms act transitively?

I'm reading and struggling with bits and pieces of the book Mal'cev, Protomodular, Homological, and Semi-Abelian categories by Borceux and Bourn. At the moment I'm having trouble with: Theorem 1.3.22 ...