Brown representability for space-valued functors
نویسندگان
چکیده
منابع مشابه
Lecture 13: Representable Functors and the Brown Representability Theorem
Let C be a category. A functor F : C → Sets is called representable if there exists an object B = BF in C with the property that there is a natural isomorphism of functors φ : C(−, BF ) −→ F. Thus, for every object X in C, there is an isomorphism φX from the set of arrows C(X,BF ) to the value F (X) of the functor. The naturality condition states that for any map f : Y → X in C, the identity F ...
متن کاملBrown Representability Does Not Come for Free
We exhibit a triangulated category T having both products and coproducts and a triangulated subcategory S ⊂ T which is both localizing and colocalizing, and for which neither a Bousfield localization nor a colocalization exists. It follows that neither the category S nor its dual satisfy Brown representability. Our example involves an abelian category whose derived category does not have small ...
متن کاملBrown Representability and Flat Covers
We exhibit a surprising connection between the following two concepts: Brown representability which arises in stable homotopy theory, and flat covers which arise in module theory. It is shown that Brown representability holds for a compactly generated triangulated category if and only if for every additive functor from the category of compact objects into the category of abelian groups a flat c...
متن کاملAuslander-reiten Theory via Brown Representability
We develop an Auslander-Reiten theory for triangulated categories which is based on Brown’s representability theorem. In a fundamental article [3], Auslander and Reiten introduced almost split sequences for the category of finitely generated modules over an artin algebra. These are short exact sequences which look almost like split exact sequences, but many authors prefer to call them Auslander...
متن کاملRepresentability in Interval-Valued Fuzzy Set Theory
Interval-valued fuzzy set theory is an increasingly popular extension of fuzzy set theory where traditional [0, 1]-valued membership degrees are replaced by intervals in [0, 1] that approximate the (unknown) membership degrees. To construct suitable graded logical connectives in this extended setting, it is both natural and appropriate to “reuse” ingredients from classical fuzzy set theory. In ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2012
ISSN: 0021-2172,1565-8511
DOI: 10.1007/s11856-012-0063-7