Operads for Symmetric Monoidal Categories

A. D. Elmendorf

This paper gives an explicit description of the categorical operad whose algebras are precisely symmetric monoidal categories. This allows us to place the operad in a sequence of four, thus generating a sequence of four successively stricter concepts of symmetric monoidal category. A companion paper will use this operadic presentation to describe a vast array of underlying multicategories for a symmetric monoidal category.

Keywords: symmetric monoidal category, operad

2020 MSC: 18M05

Theory and Applications of Categories, Vol. 39, 2023, No. 18, pp 535-544.

Published 2023-05-25.


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