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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