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Results tagged with abelian-categories
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user 78
13
votes
3
answers
2k
views
How cavalier can I be when demanding a category have direct sums?
In my meaning, a direct sum in a category should really be called a "biproduct". If $X,Y$ are objects, then a direct sum $X \oplus Y$ is an object $Z$ along with isomorphisms $\hom(Z,A) = \hom(X,A) \ …
- 54.6k
9
votes
2
answers
2k
views
What are examples of cogenerators in R-mod?
Fill in the blank, please :)
Let $\mathcal C$ be a complete and cocomplete abelian category. A generator in $\mathcal C$ is an object $X \in \mathcal C$ such that every object $Y \in \mathcal C$ …
- 54.6k
8
votes
2
answers
771
views
When is/isn't the monoidal unit compact projective?
I am interested in developing intuition for when the monoidal unit in a closed monoidal abelian category is or isn't compact projective. As such, my question is not looking for a yes/no answer, but r …
- 54.6k
9
votes
1
answer
594
views
In a closed monoidal abelian category, are the compact projectives a monoidal subcategory?
Question: In a closed monoidal abelian category such that the unit object is compact projective, must the tensor product of compact projective objects be compact projective?
Recall that an object …
- 54.6k