Duality for Clans: an Extension of Gabriel-Ulmer Duality
Jonas Frey
TL;DR
This paper extends Gabriel-Ulmer duality to clans, which encode more information than traditional finite-limit categories, by establishing a duality with certain locally finitely presentable categories.
Contribution
It introduces a duality theory between clans and locally finitely presentable categories with a specific weak factorization system, expanding the scope of Gabriel-Ulmer duality.
Findings
Established a duality between clans and enriched categories
Extended Gabriel-Ulmer duality to include additional structural information
Provides a framework for representing generalized algebraic theories
Abstract
Clans are representations of generalized algebraic theories that contain more information than the finite-limit categories associated to the locally finitely presentable categories of models via Gabriel-Ulmer duality. Extending Gabriel-Ulmer duality to account for this additional information, we present a duality theory between clans and locally finitely presentable categories equipped with a weak factorization system of a certain kind.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Algebra and Logic