Geodesic
Representable functors, Serre functors, and mutations
Izvestiya. Mathematics , Tome 35 (1990) no. 3, pp. 519-541

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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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     author = {A. I. Bondal and M. M. Kapranov},
     title = {Representable functors, {Serre} functors, and mutations},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1990_35_3_a1/}
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A. I. Bondal; M. M. Kapranov. Representable functors, Serre functors, and mutations. Izvestiya. Mathematics , Tome 35 (1990) no. 3, pp. 519-541. http://geodesic.mathdoc.fr/item/IM2_1990_35_3_a1/