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.