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David Spivak

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Category Theory - Part 1 of 6LambdaConf 20172017-05-25
Course introduces concrete definitions and verifies the claims: sets and functions, identity, initial/terminal objects, universal property axiomatizes…
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Category Theory - Part 2 of 6LambdaConf 20172017-05-25
Explains why Universal Properties, not implementations, uniquely characterize constructions: shows how an evaluation map EV and the exponential object are…
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Category Theory - Part 3 of 6LambdaConf 20172017-05-25
Covers concrete claims and examples: functors preserve identities and composition and can go between different categories; monoids model as one‑object…
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Category Theory - Part 4 of 6LambdaConf 20172017-05-25
Part 4 gives concrete translations rather than abstract slogans: it shows functors to Set as databases by writing the tables for vertices and arrows, proves…
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Category Theory - Part 5 of 6LambdaConf 20172017-05-25
Clear statement: adjunctions produce concrete maps (unit and counit) and give monads; demonstrated with concrete examples and constructions, not only words…
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Category Theory - Part 6 of 6LambdaConf 20172017-05-25
Defines Galois connections concretely: image and preimage forming a Galois connection for powersets. Shows adjunctions produce monads (unit and mu given by…
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