Talks.cam

Everything's a Kan extension - Philip Saville (University of Cambridge)
2016-01-29 11:00 - 12:00 UTC | Rainbow Room (FS07), Computer Laboratory
Kan extensions are a fundamental construction in category theory. As Mac Lane puts it, they "subsume all other fundamental concepts" in the field. I will give a brief introduction to Kan extensions: showing how the definition captures other important constructions, and how Kan extensions are hidden in many familiar examples. I will also give (largely without proof) some of the properties that make Kan extensions so useful.

Covering:

* definition of Kan extensions, their basic theory
* examples of Kan extensions
* other fundamental concepts as Kan extensions

Prerequisites:

* basic category theory (natural transformation, functor)
* some familiarity with the definition of adjunctions (I will cover this in the talk, but might be quite quick)

Material

* most of the material covered will be taken from Mac Lane's 'Categories for the Working Mathematician' (chap. X); some will come from Awodey's 'Category Theory' (esp. pp. 186-192 for the Yoneda Lemma, and pp. 208 - 234 for adjunctions and examples of Kan extensions)
* for more background the Wikipedia page on Kan extensions is pretty good; the essay at http://www.math.harvard.edu/theses/senior/lehner/lehner.pdf provides a reasonably readable introduction as well.
