## Tensors and transfors

### Sjoerd Crans – 30 April 1997

The first half of the talk I explained the mechanics of horizontal composition in \omega-teisi.
In the second half, I explored quasi-functors of two variables in terms of transfors, the corresponding tensor product, and the extent to which this might fail to give a monoidal biclosed structure. Because the conditions for composition in an \omega-tas are exactly the same as the conditions for a quasi-functors of two variables, composition is a functor C tensor C -> C, and composition with a fixed q-cell is a q-transfor. Combining this with the interpretation of tensor as (-1)-composition, one gets that tensors are transfors.
This talk was based on sections 2.4, 2.5.2 and 2.6.1 of the forthcoming 100+ page paper Central observations on \omega-teisi.

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