Questions tagged [homotopy-limits]
The homotopy-limits tag has no usage guidance.
11
questions with no upvoted or accepted answers
9
votes
0
answers
373
views
Reference for maps whose pushouts are also homotopy pushouts
Consider a category C with weak equivalences, e.g., a model category.
For the purposes of this question, let's say that a morphism f in C is an i-cofibration if any pushout (alias cobase change) ...
7
votes
0
answers
251
views
Topological localization of (infinite) inverse limits
The classical localization of topological spaces at a given set of primes $\mathcal{P}$ is a functor $\mathcal{T}\xrightarrow{(-)_{(\mathcal{P)}}}\mathcal{T}$ from a suitable category of topological ...
4
votes
0
answers
85
views
Homotopy colimits in subcategories of combinatorial model categories
We know that, in a combinatorial simplicial model category $\mathbf{M}$, we can find a regular cardinal $\lambda$ large enough that all $\lambda$-filtered homotopy colimits can be computed as strict ...
3
votes
0
answers
64
views
Homotopy limits of section spaces
Let $\mathcal{U}$ be an open cover of a topological space $B$. As we see, for example in this question, the associated Cech diagram $B_{\mathcal{U}}$ constitutes a simplicial space with the weak ...
3
votes
0
answers
168
views
Techniques for computing homotopy pullbacks
I am in the context of simplicial sets. I have a square diagram that I want to show to be homotopy pullback. What I can grasp is that it is a pullback up to some equivalences in the middle of my ...
2
votes
0
answers
92
views
Alternative construction for the loop space (?)
There is a way to realize the (infinite) loop space which relies on the (homotopy) totalization of a cosimplicial space. Given a (nice?) topological space $X$, consider the cosimplicial space $X_{\...
2
votes
0
answers
115
views
Are homotopy colimits strict?
Let's say we are working with a fibrant simplicially enriched category $\mathbf{B}$ that has all limits and all homotopy limits, and let $\mathbf{A}$ be a full subcategory that is closed under weak ...
2
votes
0
answers
135
views
Why is a homotopy limit of a cosimplicial space not the ordinary limit?
I've been trying to compute a homotopy limit of a cosimplicial object $X: \Delta \to \mathscr{M}$, where $\mathscr{M}$ is some simplicial model category, we may take it to be spaces. I'm wondering ...
2
votes
0
answers
351
views
The bar construction or the quotient for monoidal category action on a category
Given a monoid $C$ acting (from the right) on a set $M$, there is a bar construction giving a simplicial set or equivalently a translation/action category,
$$
N_\bullet (M\rtimes C)= \cdots M\times C^...
1
vote
0
answers
76
views
Homotopy limits indexed by a covering
We all know that the homotopy fiber of a continuous function $f: A \to B$ has a simple expression in terms of points and paths connecting them, that is
$$ \textrm{hofib}_y(f) = \{ (x,\gamma) \in A \...
0
votes
0
answers
108
views
Locally constant (homotopy) pre-factorization algebras
In my thesis, I'm using the theory of (homotopy) factorization algebras and particularly locally constant ones. While reading an article that I can't find again I read that already a locally constant ...