We're going to learn category theory together!

Reference: Category Theory in Context, Emily Riehl.

Schedule

• Week One (Sept. 18) — categories, properties of morphisms, duality, functors, natural transformations, equivalence of categories (§1.1 - 1.5)
• Week Two (Sept. 25) — diagram chases, representable functors, the Yoneda lemma, universality (§1.6 - 2.3)
• Week Three (Oct. 2) — introduction to limits and colimits (§3.1 - 3.2)
• Week Four (Oct. 9) — limits and colimits continued, introduction to adjunctions (§3.3 - 4.1)
• Week Five (Oct. 16) — adjunctions continued, introduction to monads ands algebras (§4.2 - 5.2)
• Week Six (Oct. 23) — monads and algebras continued, discussion on special topics and final projects (§5.3 - 5.6)
• Week Seven (Nov. 6) — more monads!!! Here are the lecture notes (§5.3 - 5.6)
• Week Eight (Nov. 13) — introduction to categorical logic. monoidal, cartesian, and closed categories
• Week Nine (Nov. 27) — introduction to topoi
• Week Ten (Dec. 4) — the (categorical) syntax of type theory and categories with families
• Week Eleven (Dec. 11) — towards higher category theory. introduction to cofibrations, fibrations, and lifting
• Week Twelve (Jan. ??) — project presentations