Question for catbul on practical use of the language of monoidal categories
I would like help on an expository point when using structures such as a tensor product in a practical situation, and where one does not want to overload the reader, and make things seem more complicated than necessary. I accept the excellent example in CFTWM p.164 2nd edition that even for the cartesian product one cannot get a strict associativity isomorphism. However when dealing say with tensor product of modules over a commutative ring, one feels that the tensor product associativity is no less strict than the usual product of sets, because of the definition by the universal bilinear property, which extends to 3-fold tensor products and trilinearity. Has this feeling been clearly expressed in the literature? Again, is there an exposition of say the tensor algebra of a vector space which adequately (in your view) takes account of coherence? I am trying to finalise an account of tensor products of crossed complexes, a much more complicated situation, but where the same ideas arise. Ronnie
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Ronnie