7 May
2008
7 May
'08
6:59 a.m.
Hi all, While we can make all monoidal categories strict, I was wondering how strict we can make monoidal functors. More precisely, given a strong monoidal functor F:(C,@,I) --> (D,*,1) between strict monoidal categories, it has the data m_xy: F(x)*F(y) ---> F(x@y) (natural) u:1 ---> F(I). Is F naturally isomorphic to a strong monoidal functor such that u is the identity? In Baez-Lauda HDA 5 it is an exercise to the reader in the proof of Proposition 8.3.6 to do this for weak monoidal categories. Cheers, David