On 2 Jan 2015, at 4:47 am, Ronnie Brown <ronnie.profbrown@btinternet.com> wrote:
Just to put a slightly different emphasis, I like to present categories and groupoids as good examples of structures having the dual roles of (i) algebraic structures in their own right, and also (ii) of value for talking about mathematical structures.
Yes, I absolutely agree (I might even replace `algebraic’ in (i) by `mathematical’). Another aspect (perhaps already mentioned) is that (monoidal) categories allow one branch of mathematics to inspire another and, indeed, talk to each other. I have in mind the recognition that concepts like dual finite dimensional vector space and trace of a linear endomorphism inspire application to knot theory; the talking is done by strong monoidal functors in explaining (in their own way) link invariants. Ross [For admin and other information see: http://www.mta.ca/~cat-dist/ ]