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Equivariant homotopy theory is the study of how homotopy theory behaves when spaces are considered together with a group action on them.

5 votes

Homotopy group action and equivariant cohomology theories

Much has already been said in the other answers and comments, but let me summarize a few points. One way to obtain from a category a 'homotopy theory' (aka an $\infty$-category) is to specify a notion …
Lennart Meier's user avatar