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Adjoint functors and tree duality [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 Graphs and ...
Jan Foniok, Claude Tardif
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Adjoint Functors and Triangulated Categories [PDF]
Communications in Algebra, 2008 We give a construction of triangulated categories as quotients of exact categories where the subclass of objects sent to zero is defined by a triple of functors. This includes the cases of homotopy and stable module categories. These categories naturally
Matthew Grime
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Transactions of the American Mathematical Society, 1958 1. Introduction. In homology theory an important role is played by pairs of functors consisting of (i) a functor Horn in two variables, contravariant in the first variable and co-variant in the second (for instance the functor which assigns to every two ...
Daniel M. Kan
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Adjoint functors and triples [PDF]
Illinois Journal of Mathematics, 1965 A riple F (F, ,) in ctegory a consists of functor F a nd morphisms la F, F F stisfying some identities (see 2, (T.1)-(T.3)) nlogous to those stisfied in monoid. Cotriples re defined dually.
Samuel Eilenberg, John C. Moore
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On Adjoint and Brain Functors [PDF]
Axiomathes, 2015 There is some consensus among orthodox category theorists that the concept of adjoint functors is the most important concept contributed to mathematics by category theory.
David Ellerman
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Properties of dense and relative adjoint functors
Journal of Algebra, 1968 In this paper we investigate some properties of dense1 and relative adjoint functors which we will use extensively in [I]. However it seems that some of these properties are of interest in themselves. Therefore we prefer not to include them in [Z] but to present them separately.
Friedrich Ulmer
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On Fundamental Constructions and Adjoint Functors [PDF]
Canadian Mathematical Bulletin, 1966 A fundamental construction of a category ζ((2), Appendice) is a triple (S, p, k), where S is a functor from ζ to itself and 2 where p:S2→S and k:1ζ→S are natural transformations such ...
J.-M. Maranda
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Adjoint functors and equivalences of subcategories
Bulletin des Sciences Mathématiques, 2003 AbstractFor any left R-module P with endomorphism ring S, the adjoint pair of functors P⊗S− and HomR(P,−) induce an equivalence between the categories of P-static R-modules and P-adstatic S-modules. In particular, this setting subsumes the Morita theory of equivalences between module categories and the theory of tilting modules.
Florencio Castaño Iglesias +2 more
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Adjoints and emergence: applications of a new theory of adjoint functors [PDF]
Axiomathes, 2007 Since its formal definition over sixty years ago, category theory has been increasingly recognized as having a foundational role in mathematics. It provides the conceptual lens to isolate and characterize the structures with importance and universality ...
David Ellerman
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Adjoint functors and derived functors with an application to the cohomology of semigroups
Journal of Algebra, 1967 In the first section of this paper we prove that, under a suitable adjointness assumption, the derived functors of certain functors on Abelian categories are equal. This theorem implies a number of results in homology theory, including the “mapping theorem” of Cartan-Eilenberg ([I], p. 150).
William W. Adams, Marc A. Rieffel
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