Solutions and Elaborations for Weibel's "Introduction to homological algebra"
While reading the book, I attempted to fill in details in proofs, perform checks, correct errors, and do exercises in the following notes. I hope they can be helpful. There are only solutions for parts of chapters 3, 4, and 8. Feel free to contact me with any corrections. Last updated 1/19/17. Link
The errata, available here, are helpful as well: Link
Injective Modules are Algebraically Closed
A slightly more concrete statement of what an injective module is.
LinkIntroductory Category Theory Notes
Notes for a series of lectures on category theory for first year graduate students.
Day 1Day 2
Day 3
Intro to Sheaves and Abelian Categories
Notes for a 2 hour talk introducing sheaves and abelian categories. Aimed at graduate students who have completed a graduate course or two in algebra and topology.
LinkSolutions to Recurrence Relations:
These notes derive the fundamental solutions associated to linear homogeneous recurrence relations using linear algebra, including the repeated eigenvalue case. The approach in these notes differs from the usual approach in that I do not use generating functions.
Link