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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.
@article{TAC_2023_39_a17, author = {A. D. Elmendorf}, title = {Operads for {Symmetric} {Monoidal} {Categories}}, journal = {Theory and applications of categories}, pages = {535--544}, publisher = {mathdoc}, volume = {39}, year = {2023}, language = {en}, url = {http://geodesic.mathdoc.fr/item/TAC_2023_39_a17/} }
A. D. Elmendorf. Operads for Symmetric Monoidal Categories. Theory and applications of categories, Tome 39 (2023), pp. 535-544. http://geodesic.mathdoc.fr/item/TAC_2023_39_a17/