## The combinatorics of higher-dimensional lax natural transformations

### Sjoerd Crans – 5 February 1997

The talk was about the second half of Chapter 3 of my PhD thesis, but with the emphasis on lax-q-transformations and their composition. In particular, I described Mike Johnson's pasting theorem, how, using this, the conditions for a lax-q-transformation can be formulated in terms of realizations of tensor products of globes with globes or with two joined globes, and I gave the mu-composition of lax-q-transformations in terms of triple tensor products of globes.
The point is that this composition is dimension-raising in such a way that omega-categories and lax-q-transformations are a, even the, prototypic weak interchange category as Mike was after last week.

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