After Thanksgiving, and I’m Stuffed…

Full of knowledge, that is. We’re nearing the end of the quarter, and as students we are almost afraid of studying anymore for fear that if we learn one more thing, it will push older knowledge out of active storage…

One of the myriad things we have been covering this fall has been set theory. Sets, collections, families, though not necessarily classes (which have a technical definition making them not sets); they are found at the beginning of almost every first year graduate course.

This gives us a kind of regular routine for various mechanisms: prove they exist (that they work on some set), then try intersections of sets – unions of sets – products – et cetera.

These same proofs are done so often, and whatever it is you are attempting so often works that someone thought of the clever idea to prove an idea once and then use it again and again. Thus we have the idea of universal objects and arrows in categories…

In Real Analysis we’ve started looking at categories via the idea of products, coproducts, and quotient maps. Similarly in Algebra, we are using Hungerford’s book, which ties everything together with the ribbon of category theory.

I hate to tease, but that’s going to have to be it for tonight. Expect another post soon discussing the basic ideas of Category Theory. (Nota bene: a very basic view, we are beginners after all!)

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