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What is a stack?

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Stacks were first discovered by Alexander Grothendieck in 1960s and they appeared in SGA 1 , Ch VIII for the first time in descent theory. Subsequently, they found application in abstract homotopy theory and later on in Gromov-Witten invariants in string theory. In Geometry they are closely related to moduli spaces. If a moduli space for some problem does not exist because of the existence of automorphisms, it may still be possible to construct a moduli stack.

I will explain why and how one might be interested in stacks from categorical point of view and illustrate few examples of stacks in category theory and topology.

References: [1] Stacks Project:

[2] Vistoli, Angela. Notes on Grothendieck topologies, fibered categories and descent theory

[3] Noohi, Behrang. A quick introduction to fibred categories and topological stacks

[4] Moerdijk, Ieke. Introduction to the language of stacks and gerbes

[5] Fulton, William. Introduction to stacks

This talk is part of the Cargo series.

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