TTF Triples in Functor Categories
نویسندگان
چکیده
We characterize the hereditary torsion pairs of finite type in the functor category of a ring R associated to tilting torsion pairs in the category of R-modules. Moreover, we determine a conditions under which they give rise to TTF triples.
منابع مشابه
Spectral triples of weighted groups
We study spectral triples on (weighted) groups and consider functors between the categories of weighted groups and spectral triples. We study the properties of weights and the corresponding functor for spectral triples coming from discrete weighted groups.
متن کاملClassification of Split Ttf-triples in Module Categories
In our work [9], we complete Jans’ classification of TTF-triples [8] by giving a precise description of those two-sided ideals of a ring associated to one-sided split TTF-triples in the corresponding module category.
متن کاملar X iv : m at h / 05 11 15 9 v 1 [ m at h . R A ] 7 N ov 2 00 5 CLASSIFICATION OF SPLIT TORSION TORSIONFREE TRIPLES IN MODULE CATEGORIES
A TTF-triple (C, T , F) in an abelian category is one-sided split in case either (C, T) or (T , F) is a split torsion theory. In this paper we classify one-sided split TTF-triples in module categories, thus completing Jans' classification of two-sided split TTF-triples and answering a question that has remained open for almost forty years.
متن کاملFuzzy projective modules and tensor products in fuzzy module categories
Let $R$ be a commutative ring. We write $mbox{Hom}(mu_A, nu_B)$ for the set of all fuzzy $R$-morphisms from $mu_A$ to $nu_B$, where $mu_A$ and $nu_B$ are two fuzzy $R$-modules. We make$mbox{Hom}(mu_A, nu_B)$ into fuzzy $R$-module by redefining a function $alpha:mbox{Hom}(mu_A, nu_B)longrightarrow [0,1]$. We study the properties of the functor $mbox{Hom}(mu_A,-):FRmbox{-Mod}rightarrow FRmbox{-Mo...
متن کاملConstructions of categories of setoids from proof-irrelevant families
When formalizing mathematics in constructive type theories, or more practically in proof assistants such as Coq or Agda, one is often using setoids (types with explicit equivalence relations). In this note we consider two categories of setoids with equality on objects and show, within intensional Martin-Löf type theory, that they are isomorphic. Both categories are constructed from a fixed proo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Applied Categorical Structures
دوره 18 شماره
صفحات -
تاریخ انتشار 2010