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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.
30
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answer
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Homotopical algebra is not concrete
There is this old result by Freyd that "homotopy is not concrete":
Freyd, Peter. "Homotopy is not concrete." The Steenrod Algebra and Its Applications: A Conference to Celebrate NE Steenrod's Six …
8
votes
2
answers
349
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Co/fibrant replacements via coend calculus
In the paper
Cordier, Jean-Marc, and Timothy Porter. "Homotopy coherent category theory." Transactions of the American Mathematical Society 349.1 (1997): 1-54.
the authors define a notion of coh …
7
votes
3
answers
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A fibrant-objects structure on Top
(Sorry for the crossposting, but I'm really interested in this question).
One can define (Paragraph 1.5, page 10) a fibrant-object structure on a suitable cartesian closed category of topological spac …
6
votes
0
answers
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Model structures on varieties of algebras
I say that a category of (say) algebras for a monad[¹] $\text{Alg}(\mathbb T)$ is "uninteresting" if the only model structures on $\text{Alg}(\mathbb T)$ result as transfer of the nine model structure …
6
votes
2
answers
334
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Model bicategories
From a conceptual point of view, the notion of a "model bicategory" is clear: a complete, cocomplete bicategory where there are two "very weak" factorization systems, where the commutativity of the sq …
4
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0
answers
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Conditions on a Quillen functor so that its comonad is homotopy-full
I am looking for an answer to the following question:
Let $F : {\cal C} \to {\cal D}$ be a left Quillen functor between combinatorial model categories; let $\tilde F \dashv \tilde G$ be the induced a …
1
vote
0
answers
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Homotopical Galois theory of coverings
In the hope this won't turn into a trivial problem (I couldn't find a similar discussion here), here's my question.
I'm studying a little homotopical algebra in this article by Brown. You can easily …