Hi! In terms of a nonzero element being defined as grouplike,is it sufficient to have **one** comultiplication such that

or does it require that to be true for every comultiplication on the space? Thank you.

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Hi! In terms of a nonzero element being defined as grouplike,is it sufficient to have **one** comultiplication such that

or does it require that to be true for every comultiplication on the space? Thank you.

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It should satisfy with being the canonical comultiplication (i. e., the one defined by for every . All the other comultiplications don’t matter.