Everything's a Kan extension

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• 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:

• Logic & Semantics for Dummies
• Rainbow Room (FS07), Computer Laboratory
• tcw57’s list
• yk373's list

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