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Everything about Ext functor
Construction in homological algebra
In mathematics, the Ext functors are the derived functors of the Hom functor. Along with the Tor functor, Ext is one of the core concepts of homological algebra, in which ideas from algebraic topology are used to define invariants of algebraic structures. The cohomology of groups, Lie algebras, and associative algebras can all be defined in terms of Ext. The name comes from the fact that the first Ext group Ext1 classifies extensions of one module by another. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Ext functorA 5-minute orientation
- Skim a recent paper: An explicit isomorphism of different representations of the Ext functor using residue currentsInfluential work since 2022
- Pick up a classic book: Commutative algebra and its connections to geometryThe most-reprinted book on the subject
- Read the landmark paper: THE OPERATORK-FUNCTOR AND EXTENSIONS OFC*-ALGEBRASCited 158 times
- Go sideways: Tor functorA closely related topic
- Go sideways: Yoneda productA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
THE OPERATORK-FUNCTOR AND EXTENSIONS OFC*-ALGEBRAS
A class ofC *-algebras and topological markov chains II: Reducible chains and the ext-functor forC *-algebras
On the functors Ext¹(E,F) for Fréchet spaces
Comments on the functor ext
Extension of the category Og and a vanishing theorem for the Ext functor for Kac-Moody algebras
Polynomial approximation of ext and tor groups in functor categories
Stable derived functors of the second symmetric power functor, second exterior power functor and Whitehead gamma functor
The Ext functor and self-sums
🆕 Influential since 2022
📚 Books worth reading
- 📕Commutative algebra and its connections to geometryPan-American Advanced Studies Institute (2009 Universidade Federal de Pernambuco) · 2011
- 📕Surveys in Representation Theory of AlgebrasAlex Martsinkovsky, Kiyoshi Igusa · 2018
- 📕Commutative AlgebraNicholas R. Baeth, Thiago H. Freitas · 2021
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Tor functor In mathematics, the Tor functors are the derived functors of the tensor product of modules over a ring. Along with the Ext functor, Tor is one of the central…
- Yoneda product In algebra, the Yoneda product (named after Nobuo Yoneda) is the pairing between Ext groups of modules: Ext n ( M , N ) ⊗ Ext m ( L , M ) → Ext n +…
- Group cohomology In mathematics (more specifically, in homological algebra), group cohomology is a set of mathematical tools used to study groups using cohomology theory…
- Derived functor In mathematics, specifically category theory, certain functors may be derived to obtain other functors closely related to the original ones. This operation…
- André–Quillen cohomology In commutative algebra and algebraic geometry, André–Quillen cohomology is a cohomology theory for commutative rings and their modules, constructed using…
- Resolution (algebra) In mathematics, and more specifically in homological algebra, a resolution (or left resolution; dually a coresolution or right resolution) is an exact…
- Exact functor In mathematics, particularly homological algebra, an exact functor is a functor that preserves short exact sequences. Exact functors are convenient for…
- Derived category In mathematics, the derived category D(A) of an abelian category A is a construction of homological algebra introduced to refine and in a certain sense…