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Results tagged with model-categories
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user 144250
A model category is a category equipped with notions of weak equivalences, fibrations and cofibrations allowing to run arguments similar to those of classical homotopy theory.
6
votes
0
answers
133
views
Are cofibrant objects flat with respect to Day convolution?
Question
Let $\mathcal{C}$ be a small symmetric monoidal category. The category $\mathsf{sSet}^{\mathcal{C}}$ of simplicial precosheaves on $\mathcal{C}$ is a symmetric monoidal model category with r …
- 3,901
0
votes
Why is the straightening functor the analogue of the Grothendieck construction?
As Xiaowen mentions, it is probably a good idea to look at the unstraightening functor for an intuition. And while Xiaowen's answer is nice, we can be even more explicit. For simplicity, I will assume …
- 2,292
7
votes
Accepted
Reference for homotopy (co)limits of (co)chain complexes via totalization of double complexes
I wrote a note for referential purposes. I hope that this will be helpful.
Arakawa, K. (2023). Homotopy Limits and Homotopy Colimits of Chain Complexes. arxiv.2310.00201
- 2,292
9
votes
1
answer
537
views
Proposition A.2.6.15 in HTT
This is a cross-post of a question in MSE.
I am reading Lurie's Higher Topos Theory and I need some help to understand a part of the proof of Proposition A.2.6.15. (A.2.6.13 in the published version …
- 15.8k