Model Theory Inspired by Modern Algebraic Geometry
A Survey of Sheaf Representations for Categorical Model Theory
Keywords:
Sheaves, Grothendieck Topoi, Categorical Logic, SchemesAbstract
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.
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Copyright (c) 2023 Gabriel Bittencourt Rios, Hugo Luiz Mariano
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