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date: 2022-02-23 18:45
modification date: Wednesday 23rd February 2022 18:45:08
title: "Classical homological algebra"
aliases: [Classical homological algebra, homological algebra]

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Last modified date: <%+ tp.file.last_modified_date() %>


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- Tags 
	- #MOC
- Refs:
	- Borcherds videos: <https://www.youtube.com/watch?v=9kAusX_AJ7Q> #resources/videos 
	-   Weibel _Homological Algebra_ #resources/books 
	-   Gelfand and Manin _Methods of Homological Algebra_ #resources/books 
	-   Kashiwara and Shapira _Categories and Sheaves_ #resources/books 
	-   Hilton and Stambach, _Homological algebra_ #resources/books 
	-   Cartan and Eilenberg, _Homological algebra #resources/books _
	-   Grothendieck, Tohoku J. paper #resources/papers 
	-   MacLane, _Homology_ #resources/books  
	-   Eisenbud _Commutative Algebra with a View Toward Algebraic Geometry_ #resources/books 
	-   Bourbaki _Commutative Algebra_ #resources/books 
	-   Atiyah and MacDonald _Commutative Algebra_ #resources/books 
	-   Zariski and Samuel, _Commutative algebra, two volumes #resources/books _ 
	-   Milnor _Introduction to algebraic K-theory_ #resources/books 
	-   Rosenberg _Introduction to algebraic K-theory_ #resources/books 
	-   Srinivas _Algebraic K-theory_ #resources/books  
	-   Mitchell _Theory of categories_ #resources/books 
	-   Freyd _Abelian categories_ #resources/books 
	-   MacLane _Categories for the working mathematician_ #resources/books 
	- [?](attachments/Lecture01.pdf)
	- [?](attachments/Modules%20and%20Categories.pdf)
	- ![Weibel Solutions](https://math.colorado.edu/~sebo2151/notes/solutions_and_elaborations.pdf)
	- The classic reference on homological algebra is Cartan and Eilenber. One may also consult Mac Lane, Rotman , Weibel , Hilton and Stammback , Bourbaki , Godement  and Grothendieck . 
		- For recent developments and many more references, see Gelfand and Manin’s excellent books. For a global perspective on the role of homological algebra in mathematics, see Dieudonne.
	- <https://server.mcm.ac.cn/~zheng/homalg.pdf>
- Links:
	- [derived category](derived category.md)
	- [Weak equivalence](Weak equivalence.md)
	- [Chain homotopy equivalence](Chain homotopy equivalence)
	- [quasiisomorphism](quasiisomorphism.md)
	- [homotopy category](homotopy category.md)
	- [Triangulated category](Triangulated category)
	- [Phantom map](Phantom map)
	- [Riemann-Hilbert correspondence](Unsorted/Riemann-Hilbert%20correspondence.md)
	- [Unsorted/sphere and disc objects in chain complexes](Unsorted/sphere%20and%20disc%20objects%20in%20chain%20complexes.md)
	- [Unsorted/projective object](Unsorted/projective%20object.md)

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# Classical homological algebra


# Unsorted

- What is the difference between the [derived category](derived category.md) and the [homotopy category](homotopy%20category.md)? #todo/questions