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arXiv · 2302.06273

Dualities in the theory of accessible categories

Giacomo Tendas
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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-Par\'e 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.

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Giacomo Tendas. 2023-02-13. Dualities in the theory of accessible categories. https://doi.org/10.1016/j.jalgebra.2025.03.012

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