Representability theorems, up to homotopy

Blanc, David; Chorny, Boris

doi:10.1090/proc/14828

Representability theorems, up to homotopy
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by David Blanc and Boris Chorny PDF

Proc. Amer. Math. Soc. 148 (2020), 1363-1372 Request permission

Abstract:

We prove two representability theorems, up to homotopy, for presheaves taking values in a closed symmetric combinatorial model category $\mathcal{V}$. The first theorem resembles the Freyd representability theorem, and the second theorem is closer to the Brown representability theorem. As an application we discuss a recognition principle for mapping spaces.

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