- Samson Abramsky and Nikos Tzevelekos: "Introduction to Categories and Categorical Logic", 2011.
- Egbert Rijke: "Introduction to Homotopy Type Theory". Part I, Martin-Löf's Dependent Type Theory, 2022, pp. i-xiii, 1-97.

- Saunders Mac Lane: "Categories for the Working Mathematician". Graduate Texts in Mathematics, volume 5, Springer New York, NY, Second Edition, Paperback, 2010. ISBN: 978-1-4419-3123-8.
- Michael Barr and Charles Wells: "Category Theory for Computing Science", Revised, 2020.

Dependent Type Theory, Dependent Function Types, Inductive Types, Identity Types, Universes.

The take-home final exam will be due Monday, May 13, 2024 during the final exam period and will be worth 34% of the grade. The take-home final exam will also have at least a two-week lead time.

Please bear in mind that everyone is expected to submit written solutions individually. That is, even if in some cases your work may be a result of group discussions, each person is responsible to write up the solutions in their own words by themselves. Please take the time to show all your work and provide a detailed explanation of your reasoning in your own words.

- Exercise 1.1.6.1bdefg on p. 17 of the first textbook.
- Exercise 1 on p. 27 of the first textbook.
- Exercise 2 on p. 27 of the first textbook.
- Prove that a coequalizer is an epimorphism.
- Show that pushouts can be constructed in terms of coproducts and coequalizers. Prove that the required universal property holds.
- Given two pushout squares placed side by side and sharing one morphism,
show that they form a larger pushout square when ignoring the inner
shared morphism. Prove that the required universal property holds.
That is,
- if maps f: C --> A, g: C --> B, and h: B --> D are given, and

- the pushout of f and g is given by i: A --> P and j: B --> P, and

- the pushout of j and h is given by k: P --> Q and m : D --> Q,

- then the pushout of f and g;h is given by i;k : A --> Q and
m : D --> Q.

- Exercise 49bd on p. 34 of the first textbook.
- Exercise 50 all on p. 34 of the first textbook.
- Exercise 1.3.5.1 on p. 35 of the first textbook.
- Exercise 1.3.5.2 on p. 35 of the first textbook.

This is the complete set of problems for Midterm #1 due in pdf in Canvas by 3 pm on Thursday, February 22, 2024.

Please bear in mind that everyone is expected to submit written solutions individually. That is, even if in some cases your work may be a result of group discussions, each person is responsible to write up the solutions in their own words by themselves. Please take the time to show all your work and provide a detailed explanation of your reasoning in your own words.

- Exercise 56 on p. 40 of the first textbook.
- Exercise 1.4.4.2 on pp. 41-42 of the first textbook.
- Exercise 1.4.4.4 on p. 42 of the first textbook.
- Exercise 1.5.5.2abc on pp. 55-56 of the first textbook.
- Exercise 1.5.5.4abc on p. 56 of the first textbook.
- Exercise 87 on p. 61 of the first textbook.
- Exercise 93 on p. 64 of the first textbook.
- Exercise 106 on p. 72 of the first textbook.
- Exercise 1.6.7.1 the first two bullets on p. 73 of the first textbook.
- Exercise 1.6.7.2 the first two bullets on p. 73 of the first textbook.

This is the complete set of problems for Midterm #2 due in pdf in Canvas by 3 pm on Monday, April 29, 2024.

Please bear in mind that everyone is expected to submit written solutions individually. That is, even if in some cases your work may be a result of group discussions, each person is responsible to write up the solutions in their own words by themselves. Please take the time to show all your work and provide a detailed explanation of your reasoning in your own words.

- Exercise 125 on p. 87 of the first textbook.
- Exercise 131 on p. 92 of the first textbook.
- Exercise 2.4ab on pp. 18-19 of the second textbook.
- Exercise 4.2abc on pp. 35-36 of the second textbook.
- Exercise 5.5ab only on pp. 49-50 of the second textbook.

This is the complete set of problems for Final Exam due in pdf in Canvas by 3 pm on Monday, May 13, 2024.