Aspects of 2-dimensional Elementary Topos Theory

PhD thesis. We contribute to expand 2-categorical elementary topos theory. In particular, we present a novel technique of reduction of the study of 2-classifiers to dense generators. We then apply it to generalize to dimension 2 the fundamental result that Grothendieck topoi are elementary topoi. In order to reach our main theorems, we produce an original calculus of colimits in 2-dimensional slices and an indexed version of the Grothendieck construction.

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