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- W4287118052 abstract "Every small monoidal category with universal finite joins of central idempotents is monoidally equivalent to the category of global sections of a sheaf of local monoidal categories on a topological space. Every small stiff monoidal category monoidally embeds into such a category of global sections. An infinitary version of these theorems also holds in the spatial case. These representation results are functorial and subsume the Lambek-Moerdijk-Awodey sheaf representation for toposes, the Stone representation of Boolean algebras, and the Takahashi representation of Hilbert modules as continuous fields of Hilbert spaces. Many properties of a monoidal category carry over to the stalks of its sheaf, including having a trace, having exponential objects, having dual objects, having limits of some shape, and the central idempotents forming a Boolean algebra." @default.
- W4287118052 created "2022-07-25" @default.
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- W4287118052 creator A5063458536 @default.
- W4287118052 date "2021-06-16" @default.
- W4287118052 modified "2023-10-16" @default.
- W4287118052 title "Sheaf representation of monoidal categories" @default.
- W4287118052 doi "https://doi.org/10.48550/arxiv.2106.08896" @default.
- W4287118052 hasPublicationYear "2021" @default.
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