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Results tagged with infinity-categories
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user 76299
Part of higher category theory that for instance in Algebraic Topology enables us to capture finer homotopic distinctions. As in say Eilenberg-Maclane spaces.
3
votes
Is there an ∞-categorical interpretation of the Quillen S⁻¹S construction?
Consider an $E_n$-monoid X. We can deloop $X$ to an $\infty$-category $\mathbf{B}X$. There's a natural functor $X^\circlearrowleft : \mathbf{B}X \rightarrow \text{Spc}$ given by the left action of $X$ …
- 2,303
1
vote
Commuting homotopy colimits and arbitrary products in spaces
I will answer my own question, in hope that it is helpful to someone.
Given a functor $X:D \rightarrow Spc$ of $\infty$-categories, we can take the unstraightening of $X$ (the appropriate generalizati …
- 30.3k
6
votes
1
answer
306
views
Commuting homotopy colimits and arbitrary products in spaces
Let $X : D \rightarrow Spc$ be a diagram with values in the $\infty$-category of spaces and $I$ some (discrete) set, not necessarily finite. ($D$ can be a 1-category if that makes statements easier, b …
- 30.3k
10
votes
1
answer
392
views
Definition of $Fun^G( \mathcal C, \mathcal D)$ in the setting of quasicategories
Our research group is currently going through the paper by Thomas Nikolaus and Peter Scholze On Topological Cyclic Homology and in the Appendix B, Proposition B.5., they use the notation $Fun^{B \math …
- 16.5k