I’ve been wanting to ask this for awhile. What, precisely, is an “antiautomorphism?” I think understanding that would help with problem 3.

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I’ve been wanting to ask this for awhile. What, precisely, is an “antiautomorphism?” I think understanding that would help with problem 3.

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Depends on the context.

An antiautomorphism of an algebra is the same as an automorphism of this algebra, except that instead of satisfying (or equivalently ) it must satisfy (or equivalently , where is the twist/flip).

An antiautomorphism of a coalgebra is the same as an automorphism of this coalgebra, except that instead of satisfying it must satisfy , where is the twist/flip.