0
votes
2answers
65 views

Are there any stable $(\infty,1)$-topoi?

Can a stable $(\infty,1)$-category be an $(\infty,1)$-topos?
2
votes
2answers
68 views

Homotopy direct limit versus direct limit

Let $X_1\to X_2\to \cdots$ be an infinite sequence of maps. Then, as I understand, the homotopy direct limit of this sequence is the space formed by taking the disjoint union of the $X_i\times I$ and ...
8
votes
1answer
97 views

How to construct a quasi-category from a category with weak equivalences?

Let $(\mathcal{C},W)$ be a pair with $\mathcal{C}$ a category and $W$ a wide (containing all objects) subcategory. Such a pair represents an $(\infty,1)$-category. One model for such gadgets is a ...
3
votes
0answers
36 views

Derived pseudo-functor

Let $ \mathfrak {X}\to \mathfrak{Y} $ be a pseudofunctor (in which $\mathfrak{X} $ is a model category and $\mathfrak{Y} $ is a bicategory). I would like to understand when there is a derived functor ...
1
vote
0answers
55 views

Torsors for 2-groups

Let $\mathbb{G}$ be a 2-group, by which I mean a strict monoidal category in which all objects are invertible (up to coherent isomorphisms) and all morphisms are invertible (strictly). What is the ...
6
votes
1answer
359 views

Can Spectra be described as abelian group objects in the category of Spaces? (in some appropriate $\infty$-sense)

I'm not a topologist and I'm trying to understand a little bit about spectra. I've been told that spectra are the homotopical version of abelian groups. Can anyone expand on this point? Apparently ...