All Questions
Tagged with equivariant-homotopy higher-category-theory
10
questions
22
votes
1
answer
1k
views
What's with equivariant homotopy theory over a compact Lie group?
For some reason -- I'm not quite sure why -- I've developed the impression that I'm supposed to "tiptoe" around equivariant homotopy theory over groups that are not finite. Should I?
Let me explain. ...
- 59k
9
votes
1
answer
365
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 \...
- 1,823
8
votes
0
answers
358
views
Is there a 2-categorical, equivariant version of Quillen's Theorem A?
Quillen's Theorem A says that a functor $F:C \to D$ (between 1-categories) induces a homotopy equivalence of classifying spaces $BC \simeq BD$ if for every object $d$ in $D$ the fiber category $F/d$ ...
- 15.3k
6
votes
3
answers
415
views
How does one rigorously lift a map $Sp \rightarrow Sp$ of spectra to equivariant spectra?
This is in part motivated from my attempt to understand tate diagonal in III.1 of Thomas Nikolaus, Peter Scholze, On topological cyclic homology, arXiv:1707.01799. I just want to make my ...
- 661
6
votes
1
answer
230
views
An induction formula for spectral Mackey functors, and a fake proof
I'm trying to get a grasp of Barwick's model for genuine $G$-spectra, that is, spectral Mackey functors 1. There's a classical formula about induction, that should be easy to prove, that I was trying ...
- 12.6k
6
votes
1
answer
332
views
What is the relationship between $O_G$-parameterized $\infty$-categories and $\infty$-categories enriched in $Top_G$?
Let $G$ be a finite group. Barwick et al define a $G-\infty$-category to be a fibration over the orbit category $O_G$ of transitive $G$-sets. But in the non-$\infty$-land, the natural guess at where I ...
- 59k
4
votes
3
answers
450
views
Need M combinatorial for existence of injective model structure on $M^G$?
I'm doing some work with model categories and operads, and to check a certain hypothesis I've had to learn a bit of equivariant homotopy theory. Let $M$ be a model category and $G$ be a finite group. ...
- 25.6k
4
votes
1
answer
208
views
Computing homotopy colimit of a space with free $S^1$-action
Context. I am trying to understand the argument in B.4 of Thomas Nikolaus, Peter Scholze, On topological cyclic homology, arXiv:1707.01799 (on p147).
I am still lost. But from Maxime's helpful ...
- 661
2
votes
1
answer
175
views
Equivariant colimit and equivariant functors
This is rather specific B.5 of Thomas Nikolaus, Peter Scholze, On topological cyclic homology, arXiv:1707.01799 (on last line p147), which I am having fundamental confusion.
We have the categories $...
- 661
2
votes
0
answers
179
views
Understanding equivariance of the Tate construction $(-)^{tC_P}$
$\DeclareMathOperator\Sp{Sp}\DeclareMathOperator\Fun{Fun}\newcommand\Cat{\text{Cat}}\DeclareMathOperator\CoInd{CoInd}\newcommand\Spaces{\text{Spaces}}$It is stated in line 10, p76, Thomas Nikolaus, ...
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