- Left adjoints preserve colimits: by hand, and by (co)Yoneda
- Symmetric sequences in Vect
- Adjunctions for the inclusion of sets into sets with idempotents
- Vector spaces as algebras over a monad
- Slice categories and limits
- Left adjoint to the Yoneda embedding

- Calculating the cohomology of a MÃ¶bius strip attached to the real projective plane
- PoincarÃ© duality and torsion
- Mapping toruses (briefly)
- Chain complexes and their morphisms
- Graded rings, and the interaction between products and cohomology
- Tor and Ext cheat sheet

My old revision notes might be of use to some of you. They are basically very concise versions of the lecture notes as they were back in 2016. **N.B.** *I have never edited these since then, so there might be some mistakes or typos, and the contents of the courses might have changed!* The courses covered in the notes are

- C2.2 Homological Algebra
- C2.7 Category Theory
- C3.1 Algebraic Topology
- C3.4 Algebraic Geometry
- C7.4 Introduction to Quantum Information