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Results tagged with ct.category-theory
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user 123439
Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.
13
votes
2
answers
2k
views
Why do we care about $(\infty,2)$-categories?
crossposted from MSE as suggested by Igor Sikora
Homotopy theory provides much motivation for studying $(\infty,1)$-categories in their relations to homotopical algebra, derived geometry, stable homot …
- 527
12
votes
1
answer
456
views
Is the Grothendieck construction a homotopy pullback?
The category of elements of a functor $F:\mathcal C\to\mathsf{Set}$ can be obtained as the strict pullback in with the forgetful functor of pointed sets $\mathsf{Set_*}\to\mathsf{Set}$:
$$
\begin{arra …
- 527
9
votes
1
answer
665
views
Two $\infty$-categories of chain complexes
In the literature, I've mostly seen two quasicategories coming from $\text{Ch}_R$:
By considering $\text{Ch}_R$ with weak equivalences $\mathcal W = \text{quasi-isomorphisms}$, we can consider its Dw …
- 527