Flat and coherent functors
نویسندگان
چکیده
منابع مشابه
Conditionally flat functors on spaces and groups
Consider a fibration sequence F → E → B of topological spaces which is preserved as such by some functor L, so that LF → LE → LB is again a fibration sequence. Pull the fibration back along an arbitrary map X → B into the base space. Does the pullback fibration enjoy the same property? For most functors this is not to be expected, and we concentrate mostly on homotopical localization functors. ...
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The starting point for the ideas in this paper is a result of Kevin Burke [2, Prop 3.2.5] in the model theory of modules. This result establishes a correspondence between syntactically defined “pp-imaginaries” and certain, coherent, functors. Specifically, fix a ring R and let R-Mod be the category of left R-modules and R-mod be the category of finitely presented left R-modules. The category of...
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such that C and D are compact objects in S (an object X in S is compact if the representable functor Hom(X,−) preserves arbitrary coproducts). The concept of a coherent functor has been introduced explicitly for abelian categories by Auslander [1], but it is also implicit in the work of Freyd on stable homotopy [9]. In this paper we characterize coherent functors in a number of ways and use the...
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We obtain semantic characterizations, holding for any Grothendieck site (C, J), for the models of a theory classified by a topos of the form Sh(C, J) in terms of the models of a theory classified by a topos [C,Set]. These characterizations arise from an appropriate representation of flat functors into Grothendieck toposes based on an application of the Yoneda Lemma in conjunction with ideas fro...
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Let A be a commutative noetherian ring. We investigate a class of functors from ≪commutative A-algebras≫ to ≪sets≫, which we call coherent. When such a functor F in fact takes its values in ≪abelian groups≫, we show that there are only finitely many prime numbers p such that pF (A) is infinite, and that none of these primes are invertible in A. This (and related statements) yield information ab...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1970
ISSN: 0021-8693
DOI: 10.1016/0021-8693(70)90136-5