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arXiv · 2609.08764

On pushouts of strict symmetric monoidal categories

Lucas Anderson·Ariel E. Rosenfield·Eric Yu
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Abstract

Toward modeling computational concurrency using the language of central idempotents in monoidal categories, we give an explicit construction of the pushout of strict symmetric monoidal categories with strong monoidal functors between them. We show that any braided strong monoidal functor strongly preserves central idempotents, and as a corollary, that the lattice of central idempotents of a symmetric monoidal category is isomorphic as a meet-semilattice to that of its strictification.

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Lucas Anderson, Ariel E. Rosenfield, Eric Yu. 2026-09-08. On pushouts of strict symmetric monoidal categories. https://arxiv.org/abs/2609.08764

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