- Tags
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Refs: #resources
- https://arxiv.org/pdf/1912.10642.pdf #resources/papers
- http://web.stanford.edu/~truax/notes/Category_Theory.pdf #resources/notes
- From categories to homotopy: https://www.math.uni-hamburg.de/home/richter/bookdraft.pdf #resources/books
- Chapter 1 https://mandal.ku.edu/M996QuillenKTheory/0TheKBooK.pdf #resources/books
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Morgan Opie’s wonderful notes #resources/notes
- Local copy: attachments/Cats1.pdf #resources/notes
- attachments/cattheory_partiii_notes.pdf #resources/notes
- attachments/Category Theory Course.pdf #resources/notes
- https://hal.archives-ouvertes.fr/hal-02184208/document #resources/notes
- https://www.asc.ohio-state.edu/green.2116/homotopyTheoryReadingCourse2020.pdf #resources/notes
- Links:
modern category theory
For DAG:
- compact
- reflexive pair
- filtered colimits
- conservative functor
Topics
-
Constructions of new categories:
- slice category
- comma category
-
Structure on categories:
- triangulated categories
- Tensored Category
- DG category
- Unsorted/enriched category
- pointed category
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Extending functors:
- Kan extension
- coend
- Day convolution
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Structure on functors
- continuous functor
- continuous functor
- span
- Object function of an equivalence of categories?
Internal Objects
- monoid object
- Unsorted/group object
- ring object
- module object
- vector space object
- algebra object
- simplicial object
Monoidal
- dualizable object of a category
- invertible object of a category
- center in a category
- compact object of a category
- Generators of a category
- linear category
- fiber functor
- tannakian
- filtered objects of a category
- graded objects of a category
- Calabi-Yau object of a category
Homotopy
^72ca2f - homotopy colimit - homotopy quotient - homotopy fixed points
Higher Cats
- higher category
- infinity categories
- stable infinity category
- presentable category
- DG category
- graded category
- whiskering
Representation Theory
- blocks of a category
- semiorthogonal decomposition
- quivers
- semisimple category