## Lax World

### Steve Lack – 12 February 1997

The idea is that there are many ``worlds'' in which one can do category theory, and that tends to look pretty similar in the different worlds if one translates notions correctly. This was rather a gentle and heuristic introduction to one such world ....
Working in the context of a general prototypic weak interchange 3-category (like a Gray-category except there is only a ``lax'' rather than a ``pseudo'' middle-four-interchange law) we defined lax monads, lax algebras, lax morphisms and so on, giving a general framework for understanding the relevant coherence conditions.

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