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Title:
What is an elementary higher topos?

Speaker:
Andre Joyal

Abstract:
There should be a notion of elementary higher topos in higher topos theory, like there is a notion of elementary topos in topos theory. We are proposing axioms partly inspired by homotopy type theory. We also give a purely categorical description of homotopy type theory.

Link:
https://www.msri.org/workshops/689/schedules/18227

Workshop:
MSRI- Reimagining the Foundations of Algebraic Topology