Adjoints- The Power of Abstraction
October 18, 2010
Bailey Hall 207
Refreshments will be served in Bailey 204 at 4:15
We will discuss the mathematical concept of adjointness (taken from category theory). The notion of adjoints appears throughout mathematics, even at the level of Math 199. We will begin by discussing examples involving partially ordered sets and Math 199 material and then gradually work our way through examples from linear algebra, abstract algebra, and more. The reason behind certain important mathematical constructions such as that of tensor product for vector spaces, free groups, commutator subgroups, and the Stone-Cech compactification will be touched on. The goal will be to argue that sometimes what may seem to be a very high, perhaps unnecessary, level of abstraction can reap unforeseen benefits in special cases.
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