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arXiv · 2610.33543

On the enriched approximate completeness

Boris Chorny·Giuseppe Leoncini
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Abstract

We generalize to the enriched setting the classical theorem of Freyd, that the free cocompletion ${\mathscr PA}$ of a category ${\mathscr A}$ is complete if and only if ${\mathscr A}$ is approximately complete. The work of Day and Lack, arXiv:math/0610439, has laid the foundations for such a generalization and has had multiple applications in homotopy theory and in category theory. Our result allows us to expand on some of these applications.

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Boris Chorny, Giuseppe Leoncini. 2026-10-24. On the enriched approximate completeness. https://arxiv.org/abs/2610.33543

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