Grothendieck-topological Group Objects
Joaquin Luna-Torres

TL;DR
This paper extends the classical theory of topological groups to finitely complete categories with Grothendieck topologies, introducing new concepts like G-topological spaces and group objects.
Contribution
It develops a categorical framework for G-topological groups, generalizing classical topological group theory to enriched categories with Grothendieck topologies.
Findings
Defined localized G-topological spaces and continuous morphisms.
Established the concepts of G-topological monoids and groups.
Provided a categorical foundation for G-topological group objects.
Abstract
In analogy with the classical theory of topological groups, for finitely complete categories enriched with Grothendieck topologies, we provide the concepts of localized G-topological space, initial Grothendieck topologies and continuous morphisms, in order to obtain the concepts of G-topological monoid and G-topological group objects.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Logic, programming, and type systems · Algebraic structures and combinatorial models
