# Topology Seminar

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Mon., Feb. 4, 2019 2:30 p.m.
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Location: Classroom Building (CL) 247
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**Speaker:** Nicholas Meadows, University of Haifa

**Title:** Descent theory and higher stacks

**Abstract:**

Classical stack theory concerns itself with glueing together objects along isomorphisms. However, I want to present a general framework which allows us to explicitly glue together objects along some kind of notion of weak equivalence (e.g. quasi-isomorphisms of complexes of sheaves, stable equivalences of spectra, etc.). The case we focus on is when our weak equivalences are those of a simplicial model category, although this can be generalized.

In particular, we show how various glueing conditions involving weak equivalences hold for presheaves of simplicial model categories satisfying an analogue of hyperdescent. The proof, which will be outlined briefly, uses the homotopy coherent nerve functor and a homotopy-theoretic description of classical stack theory due to Jardine.