22 Aug 16:06 2015

### coherence for symmetric monoidal and (co)affine categories

Paul Blain Levy <P.B.Levy <at> cs.bham.ac.uk>

2015-08-22 14:06:12 GMT

2015-08-22 14:06:12 GMT

Dear all, Given a category C, define symm(C) to be the following category: - an object is a finite family [or finite sequence, if preferred] of C-objects - a morphism from (C_i | i in I) to (D_j | j in J) consists of an bijection f : I --> J and, for each i in I, a C-morphism C_i --> D_fi. Define coaff(C) likewise but with "injection" instead of "bijection". It seems to be folklore that (1) symm(C) is the free symmetric monoidal category on C (2) coaff(C) is the free coaffine category (symmetric monoidal category with initial unit) on C. In the special case where C is discrete, these statements follow from the coherence arguments in Mac Lane's "Natural associativity and commutativity" and Petric's "Coherence in substructural categories". But for general C, where are these statements proved? Paul -- -- Paul Blain Levy School of Computer Science, University of Birmingham(Continue reading)