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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.
19
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A model category of abelian categories?
Let $\mathcal{M}$ be the following category:
The objects are small abelian categories with chosen zero object, biproducts, kernels, and cokernels.
The morphisms are functors that preserve the struct …
17
votes
1
answer
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The category theory of $(\infty, 1)$-categories
There are many proposed models for the theory of $(\infty, 1)$-categories and it has now been shown that many of these theories have Quillen-equivalent model categories, i.e. that they are equivalent …
16
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answer
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The state of the art in the rectification of homotopy-coherent structures
My question concerns rectification theorems for homotopy-coherent structures. As the meaning of this may be unclear, let me list a few examples of what I am thinking of:
Cordier and Porter proved a …
6
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0
answers
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What are the Čech-local equivalences of (simplicial pre)sheaves?
Let $\mathcal{C}$ be small category and let $J$ be a Grothendieck topology on $\mathcal{C}$. The Čech model structure on $[\mathcal{C}^\mathrm{op}, \mathbf{sSet}]$ is defined to be the left Bousfield …
6
votes
1
answer
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Left Bousfield localisation of trivial model structures
Let $\mathcal{M}$ be a category, let $\mathcal{M}^\circ$ be a reflective (full) subcategory of $\mathcal{M}$, and let $L : \mathcal{M} \to \mathcal{M}^\circ$ be the reflector.
Question.
Does there exi …
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answer
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Schwänzl and Vogt, Cofibration and fibration structures in enriched categories
In [Schwänzl and Vogt, Strong cofibrations and fibrations in enriched categories], the authors refer to an earlier preprint, [Schwänzl and Vogt, Cofibration and fibration structures in enriched catego …