# 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} }

© Foundation Compositio Mathematica, 1996, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

## 15 Citations

### Homological epimorphisms, recollements and Hochschild cohomology – with a conjecture by Snashall–Solberg in view

- Mathematics
- 2016

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

- Mathematics
- 2016

In 2009, Koenig–Nagase established a long exact sequence relating the Hochschild cohomology of an algebra with the Hochschild cohomology of the quotient of the algebra by a stratifying ideal. It is…

### The Fundamental Group of a Morphism in a Triangulated Category

- Mathematics
- 2013

We introduce the fundamental group of a morphism in a triangulated category and show that the groupoid of distinguished triangles containing a given extension of objects from an abelian category is…

### Graded Lie structure on cohomology of some exact monoidal categories

- Mathematics
- 2020

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…

### ON ALBANESE TORSORS AND THE ELEMENTARY OBSTRUCTION TO THE EXISTENCE OF 0-CYCLES OF DEGREE 1

- Mathematics
- 2006

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

- Mathematics
- 2021

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

- Mathematics
- 2003

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…

### Monoidal Categories and the Gerstenhaber Bracket in Hochschild Cohomology

- Mathematics
- 2016

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…

### Hochschild Cohomology in Algebra, Geometry, and Topology Table of Contents

- Mathematics
- 2016

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.

- Mathematics
- 2003

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…

## References

SHOWING 1-10 OF 17 REFERENCES

### Analyse et topologie sur les espaces singuliers

- Mathematics
- 1982

These volums contain s th e notes o f th e Lumin y conference : Analyse et topologie sur le s espace s singuliers . The lecture s are centere d aroun d th e following theme s : Perverse sheaves ,…

### ALGEBRAIC K-THEORY OF SPACES I

- Mathematics
- 1978

The algebraic K–theory of spaces is a variant, invented by F. Waldhausen in the late 1970’s, of the standard algebraic K–theory of rings. Until that time, applications of algebraic K–theory to…

### Higher Algebraic K-Theory of Schemes and of Derived Categories

- Mathematics
- 1990

In this paper we prove a localization theorem for the K-theory of commutative rings and of schemes, Theorem 7.4, relating the K-groups of a scheme, of an open subscheme, and of the category of those…

### Stable homotopy as a triangulated functor

- Mathematics
- 1992

Let J-I be the homotopy category of all finite spectra, ~the homotopy category of all spectra and Y--[ 89 be the homotopy category of all prime-to-2 spectra. Let H: ~--y ~ (Abelian groups) be a…

### ENHANCED TRIANGULATED CATEGORIES

- Mathematics
- 1991

A solution is given to the problem of describing a triangulated category generated by a finite number of objects. It requires the notion of "enhancement" of a triangulated category, by means of the…

### Stable homotopy and generalised homology

- Mathematics
- 1974

Preface Pt. I: S.P. Novikov's Work on Operations on Complex Cobordism 2: Cobordism groups 3: Homology 4: The Conner-Floyd Chern classes 5: The Novikov operations 6: The algebra of all operations 7:…