Skip to main content

Overview

CS6117 - Category Theory for Computer Scientists is an introduction to category theory, with a focus on material with established applications to computer science. The course will emphasize developing comfort with abstraction and instantiation while not assuming students have a strong background in mathematics.

Class Times: MWF 1:25-2:15

Location: 320 Hollister Hall

Instructor: Ross Tate
Office: 434 Gates Hall
Office Hours: Friday 9:00-10:00

Grading There will be a small homework assignment almost every week (no midterms or final):
Assignments: 100%

S/U is determined based on attendance. To receive an S, all but two lectures you miss must be the first lecture you missed that calendar week.

Piazza: http://piazza.com/cornell/spring2020/cs6117

Related Reading

Schedule

DateTopicReadingAssignments
Week 1
Jan 22 Categories, Part 1 Reference (updated throughout the semester)
Preface
3.1(ignore c), 3.2, 3.3(2b,2d-2f,4a,4c-4f), 3.4
Categories
Jan 24 Categories, Part 2 Available:
Assignment 1
Week 2
Jan 27 Categories, Part 3
Jan 29 Isomorphisms 3.8, 3.10-12, 3.13(1-2,4,6), 3.14-15
Isomorphisms		 Due:
Assignment 1
Available:
Assignment 2
Jan 31 Monomorphisms and Epimorphisms
Balanced Categories
Subobjects and Quotient Objects		 7.32, 7.33(1,3-4,9), 7.34, 7.39, 7.40(1-2,5), 7.41-42
7.49-50
7.77-81, 7.84-85, 7.86(1)
Week 3
Feb 3 Equalizers and Coequalizers
Regular Mono/epimorphisms		 7.51, 7.52(1), 7.53-55, 7.68, 7.69(1-3), 7.70
7.56-59, 7.71, 7.72(1,4), 7.73, 7.75(1), 7.76		 Available:
Assignment 3
Feb 5 Initial, Terminal, and Zero Objects
Sections and Retractions
Separators and Coseparators		 7.1, 7.2(1-2,5,8-9), 7.3-7.4, 7.5(1-3,5-6), 7.6-7.9
7.19, 7.20(4-7), 7.21, 7.24, 7.25(1,4), 7.26-27, 7.35-36, 7.42-43
7.10, 7.11(1,4-5), 7.16, 7.18(1,3,6,8)		 Due:
Assignment 2
Feb 7 Snow Day
Week 4
Feb 10 No Lecture
Feb 12 No Lecture Due:
Assignment 3
Feb 14 Duality 3.5-7 Available:
Assignment 4
Week 5
Feb 17 No Lecture
Feb 19 Functors 3.17-18, 3.20(1-4,6-8,10,13), 3.23, 3.50
Functors
Feb 21 The Category of Categories 3.24, 3.25(1), 3.26(1-3), 3.30(1)
7.2(3), 7.18(7), 7.40(6), 7.72(5), 7S(b)
3.40-43
Week 6
Feb 24 Break Available:
Assignment 5
Feb 26 Isomorphism-Preservation
Faithful/Full Functors		 3.21,3.22(2)
3.27(2-3), 3.29(2,4), 3.30-32, 7.37(2), 7.44-45, 7.28-29		 Due:
Assignment 4
Feb 28 Concrete Categories
Concrete Functors
Fibres/Fineness/Coarseness
Transportability		 5.1, 5.2(1-2,4,7), 5.3
5.9, 5.10(1-3), 5.11(2,4), 5.12, 5.14-15, 5.20
5.4(1-3), 5.5(1,3), 5.7-8, 5.18-19
5.28, 5.30(1-2)
Week 7
Mar 2 Algebras
Spaces
Coalgebras		 5.37, 5.38(1,4), 5.39
5.40-42
Coalgebras
Mar 4 (Co-)Structured Arrows
(Co-)Free Objects
(Op-)Cartesian Liftings		 8.15(1-2), 8.16(3), 8.17(1-2,6), 8.18(1), 8.19(1), 8.40(1)
8.22, 8.23(1a,3,5-6,11,13-14,16), 8.24-28, 8.40(2), 8.41(2b-2c)
8.6(1), 8.8(1,5,8,11-12), 8.9, 8.10(1), 8.11(2-3), 8.13-14		 Due:
Assignment 5
Mar 6 (Mono-)Sources
Products
(Epi-)Sinks
Coproducts		 10.1-6, 10.7(2), 10.8-10
10.19, 10.20(1-2,5-8), 10.21-30, 10.31(1,4), 10.34-37
10.62-64
10.65(1,3,6-9)		 Available:
Assignment 6
Week 8
Mar 9 Limits
Pullbacks and Intersections
Colimits
Pushouts and Cointersections		 11.1-4, 11.6-7
11.8-26
11.27, 11.28(1-2,4), 11.29
11.28(3,5), 11.30-31, 11.33
Mar 11 Internal Logic
Regular Categories		 Due:
Assignment 6
Mar 13 (Co-)Recursion Available:
Assignment 7
Week 9 - Spring Break
Week 10 - Spring Break
Week 11 - Spring Break
Week 12
Apr 6 Natural Transformations, Part 1 6.1, 6.2(2,5-6)
Apr 8 Natural Transformations, Part 2 6.6(1), 6.13-15, 6.5, 6.6(4-5), 6.17 Due:
Assignment 7
Apr 10 Natural Transformations, Part 3 6.3-4, 6A Available:
Practice 8
Week 13
Apr 13 Reflective Subcategories
Coreflective Subcategories		 4.16, 4.17(A1,B3,B7,C10-C12), 4.18-23
4.25, 4.26(A1,B4), 4.27
Apr 15 Transpositions Transpositions and Adjunctions
Apr 17 Adjunctions Available:
Practice 9
Week 14
Apr 20 Monads and Comonads 20.1-3
Monads and Comonads
Apr 22 Monad Algebras 20.4, 20.5(1-3), 20.7-11, 20.12(1-3,5-8,10)
Monad Algebras		 Available:
Practice 10
Apr 24 Effects 20B(a-c)
Kleisli Categories
Week 15
Apr 27 Multicategories Multicategories Available:
Practice 11
Apr 29 Tensors and Exponentials Tensors and Exponentials
May 1 Monoidal Categories Monoidal
For Fun: Physics, Topology, Logic and Computation: A Rosetta Stone
Week 16
May 4 Enriched Categories Enriched Categories
May 6 Toposes, Part 1
May 8 Toposes, Part 2
Week 16
May 11 Realizability Models
May 13 End of Classes
May 15 End of Classes

Homework Policies

Cornell University has a Code of Academic Integrity, with which you should be familiar. Violations of this code are treated very seriously by Cornell and can have long-term repercussions. In this course, you are encouraged to discuss the content of the course with other students, and you may also discuss homework problems with other students. However, you must do your own work, write up assignments yourself, and if you discuss a problem with another student, you are expected to document this fact in your write-up. It is a violation of the code to copy work, including programs, from other students; it is also a violation to use solutions to homework problems from previous iterations of the same course. Note that Cornell holds responsible for the code violation both the recipient and the donor of improper information.