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Alexander Gietelink Oldenziel (Jun 12 2021 at 11:34):It is well known that monoids for the Day convolution product for presheaves on the opposite of the category of finite sets and bijection (endowed with the disjoint union as monoidal product) coincide with Set-operads.
Is anything known about the comonoids for the Day convolution products?
John Baez (Jun 12 2021 at 16:58):The category of presheaves on the opposite of is usually called the category of species.
Set-operads are monoids in the category of species with its substitution tensor product. Are you really saying operads are monoids in the category of species with the Day convolution product you mention?
John Baez (Jun 12 2021 at 16:59):By the way, that Day convolution product is often called the Cauchy product of species.
Alexander Gietelink Oldenziel (Jun 13 2021 at 16:23):Dear John,
You are of course 100% right, I meant the subsitution tensor product.