9 Feb
2009
9 Feb
'09
10:26 p.m.
Dear category theorists, I have a question concerning symmetric monoidal adjunctions (of symmetric monoidal functors). Let V and W be symmetric monoidal categories, C a small category, F, G symmetric monoidal functors and F:V<-->W:G a symmetric monoidal adjunction. Is f:Fun(C,V)<-->Fun(C,W):g a symmetric monoidal adjunction? The functor categories Fun(C,V) and Fun(C,W) are endowed with the pointwise symmetric monoidal structure and the functors f and g are defined pointwise, too. I am sorry that I have to ask you all this things about monoidal categories and enriched categories but I can't find a book on that. I would be very pleased if anybody can suggest me something to read. Thank you in advance for any help. Tony