ACT
2019 John Baez ACT Lectures

Idea

• Lectures on ACT, John Baez, Azimuth Forum, 2019.

These lectures were given directly on the Azimuth forum. This is an integration of teaching and student participation, directly in the open.

The lectures refer to chapters in the following text:

• Brendan Fong and David Spivak, Seven Sketches in Compositionality: An Invitation to Applied Category Theory.

Lectures

• Lecture 1 - Introduction

• Lecture 2 - What is applied category theory

• Lecture 3 - Chapter 1: Preorders

• Lecture 4 - Chapter 1: Galois connections

• Lecture 5 - Chapter 1: Galois connections

• Lecture 6 - Chapter 1: Computing adjoints

• Lecture 7 - Chapter 1: Logic

• Lecture 8 - Chapter 1: The logic of subsets

• Lecture 9 - Chapter 1: Adjoints and the logic of subsets

• Lecture 10 - Chapter 1: The logic of partitions

• Lecture 11 - Chapter 1: The poset of partitions

• Lecture 12 - Chapter 1: Generative effects

• Lecture 13 - Chapter 1: Pulling back partitions

• Lecture 14 - Chapter 1: Adjoints, joins and meets

• Lecture 15 - Chapter 1: Preserving joins and meets

• Lecture 16 - Chapter 1: The adjoint functor theorem for posets

• Lecture 17 - Chapter 1: The grand synthesis

• Lecture 18 - Chapter 2: Resource theories

• Lecture 19 - Chapter 2: Chemistry and scheduling

• Lecture 20 - Chapter 2: Manufacturing

• Lecture 21 - Chapter 2: Monoidal preorders

• Lecture 22 - Chapter 2: Symmetric monoidal preorders

• Lecture 23 - Chapter 2: Commutative monoidal posets

• Lecture 24 - Chapter 2: Pricing resources

• Lecture 25 - Chapter 2: Reaction networks

• Lecture 26 - Chapter 2: Monoidal monotones

• Lecture 27 - Chapter 2: Adjoints of monoidal monotones

• Lecture 28 - Chapter 2: Ignoring externalities

• Lecture 29 - Chapter 2: Enriched categories

• Lecture 30 - Chapter 2: Preorders as enriched categories

• Lecture 31 - Chapter 2: Lawvere metric spaces

• Lecture 32 - Chapter 2: Enriched functors

• Lecture 33 - Chapter 2: Tying up loose ends

• Lecture 34 - Chapter 3: Categories

• Lecture 35 - Chapter 3: Categories versus preorders

• Lecture 36 - Categories from graphs

• Lecture 37 - Chapter 3: Presentations of categories

• Lecture 38 - Chapter 3: Functors

• Lecture 39 - Chapter 3: Databases

• Lecture 40 - Chapter 3: Relations

• Lecture 41 - Chapter 3: Composing functors

• Lecture 42 - Chapter 3: Transforming databases

• Lecture 43 - Chapter 3: Natural transformations

• Lecture 44 - Chapter 3: Categories, functors and natural transformations

• Lecture 45 - Chapter 3: Composing natural transformations

• Lecture 46 - Chapter 3: Isomorphisms

• Lecture 47 - Chapter 3: Adjoint functors

• Lecture 48 - Chapter 3: Adjoint functors

• Lecture 49 - Chapter 3: Kan extensions

• Lecture 50 - Chapter 3: Left Kan extensions

• Lecture 51 - Chapter 3: Right Kan extensions

• Lecture 52 - The Hom-functor

• Lecture 53 - Chapter 3: Free and forgetful functors

• Lecture 54 - Chapter 3: Tying up loose ends

• Lecture 55 - Chapter 4: Enriched protofunctors and collaborative design

• Lecture 56 - Chapter 4: Feasibility relations

• Lecture 57 - Chapter 4: Feasibility relations

• Lecture 58 - Chapter 4: Composing feasibility relations

• Lecture 59 - Chapter 4: Cost-enriched protofunctors

• Lecture 60 - Chapter 4: Closed monoidal posets

• Lecture 61 - Chapter 4: Closed monoidal posets

• Lecture 62 - Chapter 4: Enriched protofunctors

• Lecture 63 - Chapter 4: Composing enriched protofunctors

• Lecture 64 - Chapter 4: The category of enriched protofunctors

• Lecture 65 - Chapter 4: Collaborative design

• Lecture 66 - Chapter 4: Collaborative design

• Lecture 67 - Chapter 4: Feedback in collaborative design

• Lecture 68 - Chapter 4: Feedback in collaborative design

• Lecture 69 - Chapter 4: Feedback in collaborative design

• Lecture 70 - Tensoring enriched protofunctors

• Lecture 71 - Chapter 4: Caps and cups for enriched protofunctors

• Lecture 72 - Chapter 4: Monoidal categories

• Lecture 73 - Chapter 4: String diagrams and strictification

• Lecture 74 - Chapter 4: Compact closed categories

• Lecture 75 - Chapter 4: The grand synthesis

• Lecture 76 - Chapter 4: The grand synthesis

• Lecture 77 - Chapter 4: The end? No, the beginning!

Exercises

• Exercises, Azimuth Forum.

To-Do

• List the exercises on this page, with links, in correct order - like the lectures above.

• Write the exercises inline, on a separate wiki page.