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1990•Mathematics of the USSR-IzvestiyaRequires access

REPRESENTABLE FUNCTORS, SERRE FUNCTORS, AND MUTATIONS

Alexey Bondal, Mikhail M. Kapranov

Open publisher page 318 citations

Abstract

This paper studies the categorical version of the concept of mutations of an exceptional set, as used in the theory of vector bundles. The basic object of study is a triangulated category with a family of subcategories satisfying the so-called admissibility condition. A natural notion arising here is that of a Serre functor, effecting a certain duality in the triangulated category. Bibliography: 16 titles.

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What this paper is about

This paper studies the categorical version of the concept of mutations of an exceptional set, as used in the theory of vector bundles. The basic object of study is a triangulated category with a family of subcategories satisfying the so-called admissibility condition. A natural notion arising here is that of a Serre functor, effecting a certain duality in the triangulated category. Bibliography: 16 titles.

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OpenAlex reports 318 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This paper studies the categorical version of the concept of mutations of an exceptional set, as used in the theory of vector bundles. The basic object of study is a triangulated category with a family of subcategories satisfying the so-called admissibility condition. A natural notion arising here is that of a Serre functor, effecting a certain duality in the triangulated category. Bibliography: 16 titles.

Key concepts: Functor, Functor category, Natural transformation, Adjoint functors, Mathematics, Categorical variable, Derived category, Pure mathematics

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