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Results tagged with model-categories
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user 344
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.
84
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4
answers
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Do we still need model categories?
One modern POV on model categories is that they are presentations of $(\infty, 1)$-categories (namely, given a model category, you obtain an $\infty$-category by localizing at the category of weak equ …
- 25.6k
20
votes
2
answers
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Acyclic models via model categories?
Recall the acyclic models theorem: given two functors $F, G$ from a "category $\mathcal{C}$ with models $M$" to the category of chain complexes of modules over a ring $R$, a natural transformation $H …
- 25.6k
14
votes
1
answer
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The weak equivalences in the covariant model structure
Let $S$ be a simplicial set. Recall that there is a model structure, called the covariant model structure (see HTT ch. 2 and this question), on $\mathbf{SSet}/S$ such that:
The cofibrations are the …
- 25.6k