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## Everything's a Kan extensionAdd to your list(s) Download to your calendar using vCal - Philip Saville (University of Cambridge)
- Friday 29 January 2016, 11:00-12:00
- Rainbow Room (FS07), Computer Laboratory.
If you have a question about this talk, please contact Ian Orton. 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.
This talk is part of the Logic & Semantics for Dummies series. ## This talk is included in these lists:Note that ex-directory lists are not shown. |
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