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Exact functors on perverse coherent sheaves [PDF]

Compositio Mathematica, 2015
Inspired by symplectic geometry and a microlocal characterizations of perverse (constructible) sheaves we consider an alternative definition of perverse coherent sheaves. We show that a coherent sheaf is perverse if and only if $R{\rm\Gamma}_{Z}{\mathcal{F}}$ is concentrated in degree $0$ for special subvarieties $Z$ of $X$.
Clemens Koppensteiner
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The bivariant long exact sequence for the ext functor

Journal of Pure and Applied Algebra, 1975
Irwin S. Pressman
semanticscholar   +4 more sources

A characterization of final functors between internal groupoids in exact categories [PDF]

, 2017
This paper provides several characterizations of final functors between internal groupoids in Barr-exact categories. In particular, it is proved that an internal functor between groupoids is final if and only if it is full and essentially ...
Cigoli, Alan S.
core   +4 more sources

A Relationship between Left Exact and Representable Functors [PDF]

Canadian Journal of Mathematics, 1971
Our aim in this paper is to demonstrate a relationship between left exact and representable functors. More precisely, in the functor category whose objects are the additive functors from the dual of an abelian category 𝔄 to the category of abelian groups and whose morphisms are the natural transformations between them, the left exact functors can be ...
H. B. Stauffer
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Relative extriangulated categories arising from half exact functors [PDF]

Journal of Algebra, 2021
Relative theories(=closed subfunctors) are considered in exact, triangulated and extriangulated categories by Dr xler-Reiten-Smal -Solberg-Keller, Beligiannis and Herschend-Liu-Nakaoka, respectively. We give a construction method of closed subfunctors from given half exact functors which contains existing constructions. Moreover, if an extriangulated
Arashi Sakai
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On exact functors for Heller triangulated categories [PDF]

, 2013
We show certain standard constructions of the theory of Verdier triangulated categories to be valid in the Heller triangulated framework as well; viz. Karoubi hull, exactness of adjoints, localisation.
Matthias Künzer
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EXACTNESS OF COCHAIN COMPLEXES VIA ADDITIVE FUNCTORS [PDF]

, 2020
We investigate the relation between the notion of $e$-exactness, recently introduced by Akray and Zebary, and some functors naturally related to it, such as the functor $P\colon\operatorname{Mod} R\to \operatorname{Spec}(\operatorname{Mod} R)$, where $\operatorname{Spec}(\operatorname{Mod} R)$ denotes the spectral category of $\operatorname{Mod} R ...
Federico Campanini, Alberto Facchini
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Half exact functors associated with cotorsion pairs on exact categories [PDF]

Acta Mathematica Sinica, English Series, 2013
26 ...
Yu Liu
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Constructible $1$-Motives and Exactness of Realisation Functors

Documenta Mathematica, 2019
The triangulated category of cohomological 1 -motives with rational coefficients over a base scheme admits a motivic t-structure. We prove that this t-structure restricts to the subcategory of compact objects, and that pullbacks along arbitrary ...
Simon Pepin Lehalleur
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Locale morphisms with exact direct image functor in sheaves

Journal of Pure and Applied Algebra, 2005
The authors give a necessary and sufficient condition on a continuous map of locales for the induced geometric morphism between toposes of sheaves to have its direct image as well as its inverse image exact (i.e., preserving finite coproducts and epimorphisms, as well as finite limits).
F. Marmolejo, A. Merino
semanticscholar   +2 more sources