TL;DR
This paper characterizes classes of theories classified by specific types of topoi across various geometric logic fragments and explores properties of quotients of presheaf-type theories using multiple sites of definition.
Contribution
It provides new characterizations of theories classified by different topoi and leverages multiple sites to analyze quotients of presheaf-type theories.
Findings
Characterizations of theories classified by locally connected, atomic, compact, presheaf topoi.
Insights into properties of quotients of presheaf-type theories.
Use of multiple sites to establish theoretical properties.
Abstract
We give characterizations, for various fragments of geometric logic, of the class of theories classified by a locally connected (resp. connected and locally connected, atomic, compact, presheaf) topos, and exploit the existence of multiple sites of definition for a given topos to establish some properties of quotients of theories of presheaf type.
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Taxonomy
TopicsAdvanced Algebra and Logic · Rings, Modules, and Algebras