## Lawvere theories and an analogous characterisation problem

### Mark Weber – 11 March 1998

There is a nice characterisation of monoidal V-functors from a V-category M to V as monoids in the functor category [M,V] equipped with the convolution tensor product. However there is as yet no similarly nice characterisation of the strong monoidal functors. As a starting point, I have restricted to the case where M is a (V-enriched) prop and V = Vect, and I tried to establish an analogy between this problem and that of characterising the finite product preserving functors from a Lawvere theory into Set, which is well known. A fair proportion of my talk was devoted to a review of this well-established case.

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