arXiv subjects

Ariel E. Rosenfield

Publications and source records attributed to Ariel E. Rosenfield.

3 recordsLinked to original sources

arXiv2026

On pushouts of strict symmetric monoidal categories

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.

math.CT↗

arXiv2026

Hyperstructures as complete atomic Boolean algebras

We show that several categories of hyperstructures, including the mosaics of Nakamura and Reyes and the hypergroups of Marty, are realizable as categories of objects with extra structure within the category of complete atomic Boolean algebras (CABAs).

math.CT↗

arXiv2025

Enriched coverages and sheaves under change of base

We investigate how change of enriching base category via a faithful, conservative right adjoint functor interacts with enriched coverages and sheaves on a given enriched category. We prove that change of base via such a functor gives rise both to an injective mapping on subobjects in enriched presheaf categories, and to an injective mapping on enriched coverages. In case the base change functor is also full, the enriched associated sheaf construction on a presheaf category commutes with base change.

math.CT↗