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University of Cambridge > Talks.cam > Logic & Semantics for Dummies > The co-end justifies the co-means

## The co-end justifies the co-meansAdd to your list(s) Download to your calendar using vCal - Philip Saville
- Friday 19 February 2016, 11:00-12:00
- Rainbow Room (FS07), Computer Laboratory.
If you have a question about this talk, please contact Philip Saville. Ends and coends are generalisations of limits and colimits: if you think of a colimit as a generalised `sum’, then the corresponding coend is a kind of `integral’. They also have close connections to the Yoneda lemma and Kan extensions. I will recap the definitions of (co)limits, then introduce (co)ends and their basic theory. In particular, I will show how every limit is an end, and every end is a limit. Finally I will try to present examples of ends and coends at work, and show how they can be extremely useful tools for reasoning in category theory. Covering:
- recap of definition of (co)limits,
- definition of (co)ends,
- basic theory of (co)ends: relationship to limits, Fubini theorem
- (co)ends in the wild: Kan extensions, Yoneda, other examples
Prerequisites:
- basic category theory: functors, natural transformations
- I will cover the definition of limits and colimits, having some intuition already will be useful (eg. as covered in Awodey’s `Category Theory’)
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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