Random Notes
Some random notes: #todo
-Working out relative homology, an example: 
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Chain of implications for module properties:
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Definitions of common matrix groups:
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Good example of exact triangles:
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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) 389-412 403
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Many constructions in algebraic topology can be organized as solutions of fibration problems.
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What are Quillen equivalence? #todo/questions These need to preserve the model structure on each side presumably.
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More fundamental: how should one prove an equivalence of categories in general? #todo/questions
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Finding Unsorted/adjoint (categorical) is usually easy, because checking isomorphisms on hom sets is concrete.
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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
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What is the Stiefel manifold? #todo/questions
- I should write down an explicit set-theoretic description somewhere. This is definitely in Fomenko.
19:38
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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