Calendar

Topics listed in the table correspond to chapters and sections in the textbook:

Spivak, David I. Category Theory for Scientists, 2013.

Sessions 30–36 list the topics for the students’ final project presentations.

SES # TOPICS
1

1. Introduction

2. The category of sets

2.1. Sets and functions

2

2.1. Sets and functions (cont.)

2.2. Commutative diagrams

3

2.3. Ologs

2.4. Products and coproducts

4

2.4. Products and coproducts (cont.)

2.5. Finite limits in set

5 2.6. Finite limits in set (cont.)
6

2.7. Other notions in set

Mini-project: What are wiring diagrams?

7

2.7. Other notions in set (cont.)

3. Categories and functors, without admitting it

3.1. Monoids

8

3.1. Monoids (cont.)

3.2. Groups

9 3.3. Graphs (cont.)
10 3.4. Orders
11

3.4. Orders (cont.)

3.5. Databases: schemas and instances

12

4. Basic category theory

4.1. Categories and functors

13 4.1. Categories and functors (cont.)
14 4.1. Categories and functors (cont.)
15

4.1. Categories and functors (cont.)

4.2. Categories and functors commonly arising in mathematics

16 4.2. Categories and functors commonly arising in mathematics (cont.)
17 4.3. Natural transformations
18 4.3. Natural transformations (cont.)
19

4.4. Categories and schemas are equivalent , Cat ≅ Sch

5.3. Monads

20 4.5. Limits and colimits
21 4.5. Limits and colimits (cont.)
22 Discuss final project possibilities
23 4.6. Other notions in Cat
24

4.6. Other notions in Cat (cont.)

5. Categories at work

5.1. Adjoint functors

25 5.1. Adjoint functors (cont.)
26 5.1. Adjoint functors (cont.)
27 5.2. Categories of functors
28

5.2. Categories of functors (cont.)

5.3. Monads

29 5.3. Monads (cont.)
30

Student Presentation:
Logical Systems and Monoidal Categories

Student Presentation:
Meaning of Naturality in Algebra

31

Student Presentation:
The Curry-Howard Isomorphism From a Categorical Standpoint

Student Presentation:
The Limits to the General Applicability of Category Theory in Biology: Where it Works and Where It Shouldn’t

32

Student Presentation:
Notions of Computations and Monads

5.4. Operads

33

Student Presentation:
Categorizing Sloppiness

5.4. Operads (cont.)

34

Student Presentation:
An Olog for Molecular Dynamics

5.4. Operads (cont.)

35

Student Presentation:
Ologs and Proving Causality in Social Science

Student Presentation:
Illustration of Category Hilb with Examples in Atomic and Optical Physics

36

Student Presentation:
Cayley’s Theorem, Yoneda’s Lemma, and Yoneda’s Embedding

Student Presentation:
English to Olog Translation or: How I Learned to Stop Worrying and Love the Olog.

Course Info

Learning Resource Types

group_work Projects with Examples
menu_book Online Textbook
co_present Instructor Insights