Dear all, Given a V-enriched category C and sufficiently many assumptions on V and C, there is an equivalence between (symmetric) lax monoidal functors C --> V and (commutative) monoids in Fun(C,V) with respect to Day convolution. I am interested in knowing if there is a similar characterization in the literature for strong monoidal functors, as a property of objects of Mon(Fun(C,V)) or possibly BiMon(Fun(C,V)). The latter contains functors with a monoid structure for Day convolution and a comonoid structure for Day coconvolution, obtained by taking a right Kan extension in place of the usual left Kan extension in the definition of Day convolution. Best, Lorenzo You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. To take part in this conversation, reply all to this message. View group files<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.ashx?source=EscalatedMessage&action=files&GuestId=6bf90c14-94d1-45b7-a0b5-9dd447734d27> | Leave group<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.ashx?source=EscalatedMessage&action=leave&GuestId=6bf90c14-94d1-45b7-a0b5-9dd447734d27> | Learn more about Microsoft 365 Groups<https://aka.ms/o365g>