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Results tagged with ct.category-theory
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user 29322
Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.
5
votes
1
answer
170
views
Completeness of comma $\infty$-categories
Let $\mathsf{A},\mathsf{B},$ and $\mathsf{C}$ be (ordinary) categories and $F : \mathsf{A}\to\mathsf{C}$ and $G : \mathsf{B}\to\mathsf{C}$ be functors such that
$\mathsf{A}$ and $\mathsf{B}$ are comp …
- 1,349
10
votes
1
answer
732
views
Does derived hom commute with homotopy limits?
Suppose that $\mathcal{V}$ is a symmetric monoidal model category, and that $\mathcal{C}$ is a $\mathcal{V}$-enriched model category. Write $\Bbb{R}\!\operatorname{Hom}(-,-)$ for the derived Hom funct …
- 1,349
2
votes
1
answer
350
views
Are dg-modules over a cofibrant dg-category cofibrant?
Fix a commutative ring $k;$ all dg-categories will be dg-categories over $k.$ Throughout the question, I will be following the notation and conventions of Toën's "The homotopy theory of dg-categories …
- 1,349
3
votes
0
answers
260
views
Categorizing epimorphisms in $\mathscr{L}ex(\mathcal{B}^{Str},\mathsf{Set}_*)$
This is a follow up to this question of mine. The setup: Let $\mathcal{B}$ be an $\mathbb{F}_1$-linear category (Deitmar uses the term Belian); that is, $\mathcal{B}$ is pointed; balanced; contains fi …
- 1,349
11
votes
1
answer
850
views
Is $Lex(\mathcal B,\mathsf{Set}_*)$ an $\mathbb F_1$-linear category?
Following Anton Deitmar, let $\mathcal B$ be an "$\mathbb F_1$-linear category" (Deitmar uses the term "Belian"); i.e., $\mathcal B$ is balanced, pointed, contains finite products, kernels, and cokern …
- 1,349