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A model category is a category equipped with notions of weak equivalences, fibrations and cofibrations allowing to run arguments similar to those of classical homotopy theory.

8 votes
0 answers
209 views

Fibrations of orthogonal G-spectra and fixed points

There are at least two fixed point functors that characterize stable equivalences of orthogonal G-spectra: the geometric fixed points and the naive fixed points of a fibrant replacement. Is this true …
Emanuele Dotto's user avatar
7 votes
1 answer
2k views

Finite homotopy limits commute with sequential homotopy colimits

I would like to know for what kind of model category finite homotopy limits commute with sequential homotopy colimits. Would cofibrantly generated and finitely locally presentable be enough? It seems …
Emanuele Dotto's user avatar
5 votes
0 answers
205 views

Refined cofinality theorem for homotopy limits of spaces

If $C$ is a simplicial model category, $F\colon I\longrightarrow J$ a functor between small categories, and $X\colon J\longrightarrow C$ a diagram, the canonical map $holim_JX\longrightarrow holim_IX\ …
Emanuele Dotto's user avatar