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Jan Pax (Aug 24 2022 at 22:40):@John Baez I know what a center of a ring is. Is that analogously what you mean in your last comment: "center of a monoidal category" ?
John Baez (Aug 24 2022 at 22:43):The center of a monoidal category consists of objects that are "equipped with the knowledge of how to commute" with other objects - the precise definition is here:
John Baez (Aug 24 2022 at 22:44):Note that commuting is not a property anymore, it's a structure, since a monoidal category is a categorified version of a monoid.