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Results tagged with infinity-categories
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user 402
Part of higher category theory that for instance in Algebraic Topology enables us to capture finer homotopic distinctions. As in say Eilenberg-Maclane spaces.
6
votes
1
answer
817
views
Spectra and localizations of the category of topological spaces
Can we construct the category of spectra (or maybe just its homotopy category) from the category of pointed topological spaces
using some kind of localization combined with other categorical construct …
- 37.8k
4
votes
1
answer
212
views
Higher homotopy groups of Joyal fibrant replacements of 2-coskeletal simplicial sets
Suppose $X$ is a 2-coskeletal simplicial set (meaning $X^{Δ^k}→X^{∂Δ^k}$ is an isomorphism for all $k≥3$).
What is the easiest example of $X$ such that the Joyal fibrant replacement $Y$ of $X$
is not …
- 37.8k
5
votes
0
answers
428
views
Examples of nonstable ∞-categories in which sifted colimits commute with finite limits
What are some natural examples (if any) of nonstable ∞-categories in which finite limits commute with sifted colimits (or rather just colimits over Δ^op)?
Stable ∞-categories do satisfy this property …
- 37.8k
9
votes
3
answers
981
views
Reference for the Brown representability theorem in the case of locally presentable (∞,1)-ca...
Various generalizations of the Brown representability theorem
found in the literature identify additional conditions one can impose on a category $C$ so that functors $\def\op{{\sf op}}\def\Set{{\sf S …
- 37.8k
19
votes
2
answers
1k
views
Is there an ∞-categorical interpretation of the Quillen S⁻¹S construction?
The Quillen S⁻¹S construction (not to be confused with the Quillen Q-construction or the Quillen plus-construction),
as defined by Grayson in Higher algebraic K-theory: II (page 219),
takes as an inpu …
- 37.8k
13
votes
2
answers
913
views
When did the Joyal model structure on simplicial sets originate?
Some of the earliest writings on the Joyal model structure on simplicial sets include Jacob Lurie's account in Higher Topos Theory from 2006,
as well as Joyal's own account in The Theory of Quasi-Cate …
- 37.8k