The goal of this talk is to introduce the notion of a Grothendieck (\u221e, 2)-topos as a presentable (\u221e, 2)-category satisfying a categorified version of the descent axiom for (\u221e, 1)- topoi of Rezk-Lurie, which we call fibrational descent.As the name indicates, fibrational descent axiomatizes the structure of internal fibrations in an (\u221e, 2)-category and it is closely related to the straightening-unstraightening equivalence of Grothendieck-Lurie. After presenting the main definition, I will give an overview of several different ways of characterising 2-topoi, which includes a 2-dimensional version of Giraud\u2019s theorem and categorified Lawvere-Tierney axioms. Moreover, I will show how the theory of internal categories in an (\u221e, 1)-topos (as develop by Martini and Wolf) can be embedded into our formalism as (\u221e, 1)-localic 2-topoi. If time permits, I will explain how to construct a version of the Yoneda embedding in an (\u221e, 2)-topos and a theory of partially lax Kan extensions.<\/p>\n\n\n\n
Recoding: The goal of this talk is to introduce the notion of a Grothendieck (\u221e, 2)-topos as a presentable (\u221e, 2)-category satisfying a categorified version of the descent axiom for (\u221e, 1)- topoi of Rezk-Lurie, which we call fibrational descent.As the…
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