# Extension categories and their homotopy

@article{Neeman1996ExtensionCA, title={Extension categories and their homotopy}, author={Amnon Neeman and Vladimir Retakh}, journal={Compositio Mathematica}, year={1996}, volume={102}, pages={203-242} }

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## 15 Citations

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### Homological Epimorphisms and the Lie Bracket in Hochschild Cohomology

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For some exact monoidal categories, we describe explicitly a connection between topological and algebraic definitions of the Lie bracket on the extension algebra of the unit object. The topological…

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Let X be a principal homogeneous space, or torsor, under an abelian variety A over a field k. Following Lang and Tate [12], one classically associates with X two integers that give a measure of the…

### Brackets and products from centres in extension categories

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Building on Retakh’s approach to Ext groups through categories of extensions, Schwede reobtained the well-known Gerstenhaber algebra structure on Ext groups over bimodules of associative algebras…

### Homotopical structures in categories

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In this paper is presented a new approach to the axiomatic homotopy theory in categories, which offers a simpler and more useful answer to this old question: how two objects in a category (without…

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Let A be an associative and unital algebra over a commutative ring K, such that A is K-projective. The Hochschild cohomology ring HH*(A) of A is, as a graded algebra, isomorphic to the Ext-algebra of…

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In 1945 Gerhard Hochschild published On the cohomology groups of an associative algebra in the Annals of Mathematics and thereby created what is now called Hochschild theory. In 1963, Murray…

### Graded-commutativity of the Yoneda product of Hopf bimodules.

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We prove that the Yoneda product for Hopf bimodule extensions is gradedcommutative and we give a candidate for a graded Lie bracket on the cohomology of Hopf algebras defined by Gerstenhaber and…

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