Random Notes
Some random notes: #todo
-Working out relative homology, an example: attachments/image_2021-04-25-01-52-05.png❗
-
Chain of implications for module properties:
attachments/image_2021-04-25-01-52-56.png❗ -
Definitions of common matrix groups:
attachments/image_2021-04-25-01-53-18.png❗ -
Good example of exact triangles:
attachments/image_2021-04-25-01-53-49.png❗ -
Manifolds from the sheaf perspective, a reference:
attachments/image_2021-04-25-01-54-21.png❗
Random Algebraic Topology
Reference: paper on “constructive” algebraic topology J. Rubio, F. Sergeraert / Bull. Sci. math. 126 (2002) 389-412 403
-
Many constructions in algebraic topology can be organized as solutions of fibration problems.
-
What are Quillen equivalence? #unanswered_questions These need to preserve the model structure on each side presumably.
-
More fundamental: how should one prove an equivalence of categories in general? #unanswered_questions
-
Finding adjunction 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. #unanswered_questions
-
What is the Stiefel manifold? #unanswered_questions
- I should write down an explicit set-theoretic description somewhere. This is definitely in Fomenko.
19:38
-
Is there a natural exact sequence associated to a composition series? #unanswered_questions
- This seems like it should be super easy, we have quotients everywhere.
- Is there a precise relation to iterated extensions..? #unanswered_questions