Work

Dualities in the theory of accessible categories

Year: 2025

Type: article

Abstract: Through the notion of weakly sound class of weights, we recover many known dualities involving accessible categories with a chosen class of limits, as instances of a general duality theorem. These include the Gabriel–Ulmer duality for locally finitely presentable categories, Diers duality for locally finitely multipresentable categories, and the Makkai–Paré duality for finitely accessible categories. In doing so, we extend these to the enriched setting, provide a more formal and unifying approach to the theory, and also discuss new dualities that arise as a consequence of our main theorem.

Source: Journal of Algebra

DOI: 10.1016/j.jalgebra.2025.03.012

Author: Giacomo Tendas

Institution: University of Manchester

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,310

Funders: Grantová Agentura České Republiky, Engineering and Physical Sciences Research Council