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On pushouts of strict symmetric monoidal categories
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.
Related
BibTeX
@misc{anderson2026pushouts,
title = {{On pushouts of strict symmetric monoidal categories}},
author = {Lucas Anderson and Ariel E. Rosenfield and Eric Yu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08764},
eprint = {2609.08764},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08764},
}
RIS
TY - UNPB
TI - On pushouts of strict symmetric monoidal categories
AU - Lucas Anderson
AU - Ariel E. Rosenfield
AU - Eric Yu
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08764
UR - https://arxiv.org/abs/2609.08764
AB - 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.
ER -