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Dec 4, 2021 at 13:50 comment added Simon Henry Oh... I should have known this one ! Sorry about this. I actually discarded it because I thought is was a simplicially enriched enriched adjunction... but it is not, I was just being confused. My mistake was that if C is a (nice enough) simplicially enriched category then monoid in C is indeed also simplicial... but that only work if you take monoid for the cartesian structure (and product are compatible to the simplicial enrichement), not monoid for another tensor product...
Dec 4, 2021 at 13:38 vote accept Simon Henry
Dec 4, 2021 at 11:41 history answered David White CC BY-SA 4.0