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7
votes
1
answer
289
views
Is any abelian category a subcategory of $\mathrm{Ab}^I$?
Motivation: define a concrete Abelian category as a category with a univalent and injective functor in $\mathrm{Ab}^I$ (such that all homological concepts in it coincide with simple set-theoretic conc …
9
votes
1
answer
643
views
What are abelian categories enriched over themselves?
As far as I understand, an arbitrary abelian category is not enriched over itself, for example, $\mathrm{ChainComplex}(\mathrm{Ab})$ is, right? On the other hand, the categories $\mathrm{Mod}(R)$ (in …
8
votes
1
answer
398
views
Is the category of chain complexes a reflexive or coreflexive subcategory of the category of...
Let $A$ be an abelian category (you can assume additional conditions for its goodness). Let $\mathrm{Seq}(A) = \mathrm{Func}(\mathbb{Z}, A)$, where $\mathbb{Z}$ is the standard order category on integ …