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arXiv · 2606.26717

Isoregular theories, accessible 2-categories, and free constructions

Nicola Gambino·Giacomo Tendas
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Abstract

We introduce isoregular theories, in which it is possible to express existential quantification up to unique isomorphism, as typically used to characterise category-theoretic universal constructions, such as limits. We then develop a functorial semantics for isoregular theories and prove that their 2-categories of models are accessible with flexible limits. We apply these results by showing that a number of 2-categories of interest in general category theory, categorical algebra, and categorical logic are models of isoregular theories, thereby establishing that they are accessible 2-categories with flexible limits and obtaining a number of new free constructions.

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Nicola Gambino, Giacomo Tendas. 2026-06-25. Isoregular theories, accessible 2-categories, and free constructions. https://arxiv.org/abs/2606.26717

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