2-classifiers via dense generators and Hofmann-Streicher universe in stacks
| Autor: | Mesiti, Luca |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We expand the theory of 2-classifiers, that are a 2-categorical generalization of subobject classifiers introduced by Weber. The idea is to upgrade monomorphisms to discrete opfibrations. We prove that the conditions of 2-classifier can be checked just on a dense generator. The study of what is classified by a 2-classifier is similarly reduced to a study over the objects that form a dense generator. We then apply our results to the cases of prestacks and stacks, where we can thus look just at the representables. We produce a 2-classifier in prestacks that classifies all discrete opfibrations with small fibres. Finally, we restrict such 2-classifier to a 2-classifier in stacks. This is the main ingredient of a proof that Grothendieck 2-topoi are elementary 2-topoi. Our results also solve a problem posed by Hofmann and Streicher when attempting to lift Grothendieck universes to sheaves. Comment: Accepted in Canadian Journal of Mathematics |
| Databáze: | arXiv |
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