Re: Reading advice

From: "Prof. J. Lambek" <lambek@math.mcgill.ca> Subject: categories: Reading advice

Concerning the question by Lindquist:

The tensor product automatically satisfies all functoriality, associativity and coherence conditions, if it is introduced by a universal property as by Bourbaki.

In view of this would it be fair to say that coherence is not a notion intrinsic to category theory, but rather arises from the traditional set theoretic presentation (or at least point of view) of category theory? Much the same can surely be said of naturality, whose abstract essence is that of 2-cells but which is standardly presented concretely, where the interchange axiom becomes a not entirely trivial theorem. Vaughan Pratt