Dear Andre, Your argument applies equally well beyond mathematics, to other sciences/practices wherever categorical structure is natural. I met Fred at my first CT, in 99, and immediately he made one feel welcome. Best wishes, Bob.
On 11 Sep 2017, at 17:19, Joyal, André <joyal.andre@uqam.ca> wrote:
Dear John, and category theorists,
The fact that every category has an opposite introduces a symmetry in mathematics that would not be there otherwise. The category of sets is not self dual, but a disjoint union of sets is a coproduct, dual to a product.
Thurston does not show esteem for logic. Most mathematicians are taking logic for granted; they just use it as a part of their natural language. It is obvious that human understanding depends on the the laws of thought, on logic. In a sense, category theory is a branch of mathematical logic, since it greatly improves mathematical thinking in general. A category theorist might say (not too loudly) that mathematical logic is a branch of category theory.
Best, andré
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