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Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.

5 votes

singly-generated monoids in mathematics

While reading your question I was reminded of Kuratowski's closure-complement problem. Here we start with an arbitrary subset $X$ of a topological space, and are allowed to apply the two operations o …
Tony Huynh's user avatar
  • 32.1k
8 votes

Does the hypergraph structure of the set of subgroups of a finite group characterize isomorp...

To expand on Steve D's comment, the answer is indeed yes for finite abelian groups. The following is a simplified version of an earlier proof (rendering some of the below comments obsolete). Proof. …
Tony Huynh's user avatar
  • 32.1k
18 votes
Accepted

Category theoretic interpretation of matroids?

If I understand your question correctly, I believe that the problem is still open. That is, if we let $\mathcal{M}$ be the category of (simple) matroids, where the morphism are given by strong maps, t …
Tony Huynh's user avatar
  • 32.1k