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Modules as exact functors [PDF]

, 2018
We can define a module to be an exact functor on a small abelian category. This is explained and shown to be equivalent to the usual definition but it does offer a different perspective, inspired by the notions from model theory of imaginary sort and ...
Prest, Mike
core   +8 more sources

The exact functor theorem for ${BP_* }/ {I_n }$-theory [PDF]

Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1976
Nobuaki Yagita
semanticscholar   +5 more sources

Preservation of Loewy Diagrams Under Exact Functors [PDF]

Journal of Pure and Applied Algebra, 2023
Minor ...
Matthew Rupert
openalex   +4 more sources

Nakayama’s lemma for half-exact functors [PDF]

Proceedings of the American Mathematical Society, 1972
We prove an analog of Nakayama's Lemma, in which the finitely generated module is replaced by a half-exact functor from modules to modules. As applications, we obtain simple proofs of Grothendieck's "property of exchange" for a sheaf of modules under base change, and of the "local criterion for flatness." 1. Nakayama's Lemma.
Arthur Ogus, George M. Bergman
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Non-exact integral functors [PDF]

Bulletin of the London Mathematical Society, 2012
We give a natural notion of (non-exact) integral functor in the context of k-linear and graded categories. In this broader sense, we prove that every k-linear and graded functor is integral.
Fernando Sancho de Salas
openalex   +4 more sources

Exactness and faithfulness of monoidal functors [PDF]

Confluentes Mathematici, 2023
Inspired by recent work of Peter O’Sullivan, we give a condition under which a faithful monoidal functor between abelian ⊗-categories is exact.
Bruno Kahn
openalex   +4 more sources

Satellites of Half Exact Functors, A Correction [PDF]

Proceedings of the American Mathematical Society, 1964
In Chapter III of H. Cartan and S. Eilenberg, Homological algebra, there is the substantial THEOREM 3.1. Let (1) O A' A A" O be an exact sequence. If T is a covariant half exact functor then the sequence (2) * * * Sn-S T(A") SnT(A') SnT(A) Sn T(A") Sn+'T(A') >... is exact. For T contravariant, A' and A" should be interchanged. The proof, which occupies
Harley Flanders
  +5 more sources

Exact Embedding Functors and Left Coherent Rings [PDF]

Proceedings of the American Mathematical Society, 1988
Let R R and S S be rings with unit. Suppose P P is a free R R -module on β \beta generators, where β \beta is an infinite cardinal number not smaller than the cardinality of R R , and T T is the ring of ...
Kent R. Fuller, George Hutchinson
openalex   +2 more sources

Flat functors and free exact categories [PDF]

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1996
AbstractLet C be a small category with weak finite limits, and let Flat(C) be the category of flat functors from C to the category of small sets. We prove that the free exact completion of C is the category of set-valued functors of Flat (C) which preserve small products and filtered colimits. In case C has finite limits, this gives A. Carboni and R. C.
Hongde Hu
openalex   +3 more sources

On stable equivalences induced by exact functors [PDF]

Proceedings of the American Mathematical Society, 2005
Let A A and B B be two Artin algebras with no semisimple summands. Suppose that there is a stable equivalence α \alpha between A A and B B such that α \alpha is induced by exact functors.
Yuming Liu
openalex   +2 more sources