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Session S27 - Categories and Topology

Thursday, July 15, 12:00 ~ 12:30 UTC-3

A higher Grothendieck construction

Matias del Hoyo

Universidade Federal Fluminense, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In joint work with G. Trentinaglia, motivated by the study of Lie groupoids, we develop a construction relating simplicial vector bundles and representations up to homotopy. Our construction can be seen both as a higher analog of the Grothendieck correspondence between fibered categories and pseudo-functors in Cat, and also as a relative version of classic Dold-Kan correspondence between simplicial objects and chain complexes. In this short talk, I will briefly discuss the background, present our formulas, and mention some applications.

Joint work with Giorgio Trentinaglia (Instituto Superior Técnico, Portugal).

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