Categories enriched over symmetric closed multicategories

Volodymyr Lyubashenko

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arXiv · 2304.11227

Categories enriched over symmetric closed multicategories

Volodymyr Lyubashenko

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Abstract

We construct a machine which takes as input a locally small symmetric closed complete multicategory $\mathsf V$. And its output is again a locally small symmetric closed complete multicategory $\mathsf V\text-\mathcal{C}at$, the multicategory of small $\mathsf V$-categories and multi-entry $\mathsf V$-functors. An example of such $\mathsf V$ is provided by short spaces (vector spaces with a system of seminorms) and short maps. When the ground multicategory $\mathsf V$ is $\mathsf{Set}$ we obtain strict 2-categories and their surroundings by iterating twice the construction of categories.

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BibTeX RIS

Volodymyr Lyubashenko. 2023-04-21. Categories enriched over symmetric closed multicategories. https://arxiv.org/abs/2304.11227

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