Spring 2013 -- CT4S, what we cover

David Spivak

Research Scientist
Department of Mathematics
MIT

Office: 2-230
Email: dspivak--math/mit/edu

18-S996,  Spring 2013:
Category theory for scientists


What we've covered and hope to cover:


Class numberDateSections from CT4S book
1.Feb 61. Introduction.
2. The category of sets.
2.1. Sets and functions.
2.Feb 8(MIT closed and class canceled due to storm.)
3.Feb 112.1. Sets and functions.
2.2 Commutative diagrams.
4.Feb 132.3. Ologs.
2.4. Products and coproducts.
5.Feb 152.4. Products and coproducts.
2.5. Finite limits in Set.
6.Feb 192.6. Finite colimits in Set.
7.Feb 202.7. Other notions in Set.
Mini-project: what are wiring diagrams?
8.Feb 222.7. Other notions in Set.
3. Categories and functors, without admitting it.
3.1. Monoids.
9.Feb 253.1. Monoids.
3.2. Groups.
10.Feb 273.3. Graphs.
11.Mar 13.4. Orders.
12.Mar 43.4. Orders.
3.5. Databases.
13.Mar 64. Basic category theory.
4.1. Categories and functors.
14.Mar 84.1. Categories and functors.
15.Mar 114.1. Categories and functors.
16.Mar 134.1. Categories and functors.
4.2. More basic examples from mathematics.
17.Mar 154.2. More basic examples from mathematics.
18.Mar 184.3. Natural transformations.
19.Mar 204.3. Natural transformations.
20.Mar 224.4. Categories and schemas are equivalent.
5.3. Monads (quick tour).
21.Apr 14.5. Limits and colimits.
22.Apr 34.5. Limits and colimits.
23.Apr 5Discuss project possibilities.
24.Apr 84.6. Other notions in Cat.
25.Apr 104.6. Other notions in Cat.
5. Categories at work.
5.1. Adjunctions.
26.Apr 125.1. Adjunctions.
27.Apr 17 5.1. Adjunctions.
28.Apr 19 (MIT closed and class canceled due to Boston lockdown.)
29.Apr 22 5.2. Categories of functors.
30.Apr 24 (MIT classes canceled due to "day of reflection.")
31.Apr 26 5.2. Categories of functors.
5.3. Monads.
32.Apr 295.3. Monads.
33.May 1Presentation by Yair Shenfeld: Logical systems and Monoidal Categories.
Presentation by Whan Ghang: Meaning of Naturality in Algebra.
34.May 3Presentation by Jason Gross: The Curry-Howard Isomorphism from a Categorical Standpoint.
Presentation by William Yu: On the limits to the general applicability of category theory in biology: where it works and where it shouldn't.
35.May 6Presentation by Daniel Huang: Notions of Computations and Monads.
5.4. Operads.
36.May 8Presentation by Leon Dimas: Categorizing sloppiness.
5.4. Operads.
37.May 10Presentation by Dieter Brommer: An olog for molecular dynamics.
5.4. Operads.
38.May 13Presentation by Noam Angrist: Ologs and proving causality in social science.
Presentation by Wenjie Ji: Illustration of Category Hilb with examples in atomic and optical physics.
39.May 15Presentation by Aaron Brookner: Cayley's theorem, Yoneda's lemma, and Yoneda's embedding.
Presentation by Dylan Erb: English to Olog Translation or: how I learned to stop worrying and love the Olog.

Original course announcement.



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