-tuply monoidal -categories certainly crop up in nature! How could they not?
]]>I see we have k-tuply monoidal (n,r)-category. Do they crop up in nature?
I mostly only wrote that to record the insight that the concept still makes sense when (giving the concept of -tuply groupal -groupoid).
]]>Something I may have asked before, but we seem to deal with -categories with various properties assigned to certain intervals of -morphisms; no property, has duals, is invertible, is trivial. So we may say ’invertible above ’, or ’trivial above and below perhaps with duals between. How far do they ever get combined? I see we have k-tuply monoidal (n,r)-category. Do they crop up in nature? How about a k-tuply monoidal (infinity,n)-category with duals?
]]>You defined “has adjoints” twice. It seems to me that the first should have been for -morphisms and I changed it accordingly.
]]>stub for (infinity,n)-category with duals
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