Random Notes
Some random notes: #todo
Working out relative homology, an example:

Chain of implications for module properties:

Definitions of common matrix groups:

Good example of exact triangles:

Manifolds from the sheaf perspective, a reference:
Random Algebraic Topology
Reference: paper on “constructive” algebraic topology J. Rubio, F. Sergeraert / Bull. Sci. math. 126 (2002) 389412 403

Many constructions in algebraic topology can be organized as solutions of fibration problems.

What are Quillen equivalence? #todo/questions These need to preserve the model structure on each side presumably.

More fundamental: how should one prove an equivalence of categories in general? #todo/questions

Finding Unsorted/adjoint (categorical) is usually easy, because checking isomorphisms on hom sets is concrete.

If you just have a random functor, does it even have right or left adjoints in general? There must be theorems about this. See adjoint functor theorem. #todo/questions

What is the Stiefel manifold? #todo/questions
 I should write down an explicit settheoretic description somewhere. This is definitely in Fomenko.
19:38

Is there a natural exact sequence associated to a composition series? #todo/questions
 This seems like it should be super easy, we have quotients everywhere.
 Is there a precise relation to iterated extensions..? #todo/questions