Categories Bartosz Milewski Youtube notes

Part I

I - 1.1: Motivation and Philosophy - 46:46
I - 1.2: What is a category? - 48:18
I - 2.1: Functions, epimorphisms - 46:14
I - 2.2: Monomorphisms, simple types - 24:34
I - 3.1: Examples of categories, orders, monoids - 48:26
I - 3.2: Kleisli category - 41:58
I - 4.1: Terminal and initial objects - 47:47
I - 4.2: Products - 34:49
I - 5.1: Coproducts, sum types - 36:47
I - 5.2: Algebraic data types - 33:14
I - 6.1: Functors - 54:10
I - 6.2: Functors in programming - 51:36
I - 7.1: Functoriality, bifunctors - 56:32
I - 7.2: Monoidal Categories, Functoriality of ADTs, Profunctors - 49:15
--- end of current notes ---
I - 8.1: Function objects, exponentials - 45:25
I - 8.2: Type algebra, Curry-Howard-Lambek isomorphism - 20:56
I - 9.1: Natural transformations - 51:27
I - 9.2: bicategories - 43:04
I - 10.1: Monads - 1:15:29
I - 10.2: Monoid in the category of endofunctors - 32:57

Part II

II - 1.1: Declarative vs Imperative Approach - 36:17
II - 1.2: Limits - 48:26
II - 2.1: Limits, Higher order functors - 42:36
II - 2.2: Limits, Naturality - 28:53
II - 3.1: Examples of Limits and Colimits - 41:48
II - 3.2: Free Monoids - 36:54
II - 4.1: Representable Functors - 50:19
II - 4.2: The Yoneda Lemma - 36:11
II - 5.1: Yoneda Embedding - 50:53
II - 5.2: Adjunctions - 40:36
II - 6.1: Examples of Adjunctions - 48:25
II - 6.2: Free-Forgetful Adjunction, Monads from Adjunctions - 37:15
II - 7.1: Comonads - 37:39
II - 7.2: Comonads Categorically and Examples - 44:05
II - 8.1: F-Algebras, Lambek's lemma - 51:39
II - 8.2: Catamorphisms and Anamorphisms - 42:27
II - 9.1: Lenses - 41:5911
II - 9.2: Lenses categorically - 43:42

Part III

III - 1.1: Overview part 1 - 26:59
III - 1.2: Overview part 2 - 28:12
III - 2.1: String Diagrams part 1 - 29:08
III - 2.2: String Diagrams part 2 - 32:15
III - 3.1: Adjunctions and monads - 25:48
III - 3.2: Monad Algebras - 28:31
III - 4.1: Monad algebras part 2 - 26:55
III - 4.2: Monad algebras part 3 - 29:02
III - 5.1: Eilenberg Moore and Lawvere - 29:55
III - 5.2: Lawvere Theories - 29:26
III - 6.1: Profunctors - 29:14
III - 6.2: Ends - 34:26
III - 7.1: Natural transformations as ends - 33:36
III - 7.2: Coends - 43:15

Original resources
from Bartosz Milewski

Youtube playlist - Part I (20 videos, ~ 15h).
Youtube playlist - Part II (18 videos, ~ 10h30).
Youtube playlist - Part III (18 videos, ~ 7h).

Blog : Category Theory for Programmers : the preface
PDF book (~ 500 pages)
Tex source of the pdf book
Paper book at lulu.com (452 pages)

Started in 2018 by Thierry Graff.
These notes helped me to follow the first chapters of the course, but do not bring new information - see Milewski's blog and book for complementary resources.
There are notes until part I, chapter 7.2 ; for the moment, I stopped watching the videos (because I bought the book).
You can download these notes from github.com/tig12/milewski-youtube-notes.

The notes are written in english but I use french conventions for capitalization and spaces.
- The characters ; : ? ! are preceeded and followed by a white space.
- Names of months, weekdays, languages etc. are not capitalized.

Category Theory for programmers

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