7 Feb
2008
7 Feb
'08
8:05 p.m.
Let F be a functor from a monoidal category M to a category S. We are given beta(p,a) : F(p) --> F(p*a) natural in p,a in M. If I tell you that, in addition to naturality, beta is "monoidal", I'm sure you will immediately guess what I mean by this, viz. (a) for any p,a,b in M beta(p,a) ; beta(p*a,b) = beta(p,a*b) ; F(alpha(p,a,b)) (b) for any p in M beta(p,1) = F(rho(p)) Yet I cannot see any reason for giving the name "monoidality" to (a)-(b). It doesn't appear to be a monoidal natural transformation in the official sense. There are no monoidal functors in sight. Can somebody please justify my usage? Paul