Model Theory Inspired by Modern Algebraic Geometry: A Survey of Sheaf Representations for Categorical Model Theory

Gabriel Bittencourt Rios; Hugo Luiz Mariano

doi:10.14244/lajm.v2i01.8

Authors

Gabriel Bittencourt Rios University of Toulouse III
Hugo Luiz Mariano Universidade de São Paulo

DOI:

https://doi.org/10.14244/lajm.v2i01.8

Keywords:

Sheaves, Grothendieck Topoi, Categorical Logic, Schemes

Abstract

In this survey, we expound sheaf representations of categories in the context of categorical logic. Namely, we present classifying topoi of coherent theories in terms of equivariant sheaves of groupoid (and then explore the generalization of this technique to a more general categorical context); expose a representation of Grothendieck topoi as global sections of sheaf and, finally, show a quick introduction to logical schemes, a proposed model-theoretic analogue to the schemes of Algebraic Geometry.

Author Biography

Hugo Luiz Mariano, Universidade de São Paulo

Professor associado, Instituto de Matemática e Estatística

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