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Luca Mesiti - 迈向基本2-拓扑斯
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https://youtu.be/keWb__gt2gk Luca Mesiti Towards elementary 2-toposes In this talk we will discuss which axioms we should require for a good notion of 2-categorical elementary topos. 2-dimensional elementary topos theory has originated with the work of Weber, who proposed to upgrade subobject classifiers to discrete opfibration classifiers. In the archetypal case of Cat, the discrete opfibration classifier is exhibited by the Grothendieck construction, suggesting that we can think of 2-dimensional classifiers as internal Grothendieck constructions in a 2-category. The theory of elementary 2-toposes has then been further developed in my PhD thesis, where I proposed a stronger better-behaved notion of discrete opfibration classifier called good 2-classifier. We will see that a powerful theorem of reduction of the study of 2-dimensional classifiers to dense generators provides a good 2-classifier in the 2-category of stacks over a site. Exactly as sheaves give Grothendieck toposes, stacks give 2-dimensional Grothendieck toposes and they should thus be a preeminent example of elementary 2-topos. We can then study this preeminent example to try and understand which further axioms we should require to reach a notion of elementary 2-topos.
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