Operads for Symmetric Monoidal Categories

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