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Results tagged with model-categories
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user 11546
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.
3
votes
2
answers
308
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Free Monoids in Closed Symmetric Monoidal Categories
There appear to be questions perhaps tangentially related to this that have been asked already. If so a reference and a close would be heartily appreciated.
Give some category $\mathcal{C}$ with the …
- 10.5k
8
votes
1
answer
438
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Monoidal Model Categories with Suspension Functor
This is basically just me trying to find out what such categories are called, and where they are written about. If I think of some model category of spectra being a "stabilization" of some model cate …
- 10.5k
6
votes
1
answer
280
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What structure of a monoidal simplicial model category is preserved by taking the opposite c...
Suppose we have $(M,\otimes,1)$, a monoidal simplicial model category. Then we can consider the opposite model category $M^{op}$ with the opposite model structure (fibrations become cofibrations, etc. …
- 10.5k
14
votes
1
answer
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Non-Cartesian Monoidal Model Structure on a Slice Category
Given a monoidal model category $(M,\otimes, 1)$, and a monoid therein $A$, one can take the slice model category $M_{/A}$. This category has a natural monoidal structure induced by taking fibered pro …
- 10.5k
10
votes
1
answer
476
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When is a quasicategory over $N(\Delta)^{op}$ a planar $\infty$-operad?
In Lurie's DAG II, a notion of monoidal $\infty$-category is given that differs from the notion given in his later book Higher Algebra. In the former, the relevant structure is a cocartesian fibratio …
- 10.5k
5
votes
Accepted
When is a quasicategory over $N(\Delta)^{op}$ a planar $\infty$-operad?
So, this ends up being simpler than I realized, and is in some sense this question's existence is purely a result of me not reading the above cited DAG II closely enough.
In the first section of DAG …
- 10.5k