منابع مشابه
A Generalization of Watts’s Theorem: Right Exact Functors on Module Categories
Watts’s Theorem says that a right exact functor F : ModR → ModS that commutes with direct sums is isomorphic to − ⊗R B where B is the R-S-bimodule FR. The main result in this paper is the following: if A is a cocomplete category and F : ModR→ A is a right exact functor commuting with direct sums, then F is isomorphic to − ⊗R F where F is a suitable R-module in A, i.e., a pair (F , ρ) consisting...
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For a broad collection of categories K, including all presheaf categories, the following statement is proved to be consistent: every left exact (i.e. finite-limits preserving) functor from K to Set is small, that is, a small colimit of representables. In contrast, for the (presheaf) category K = Alg(1, 1) of unary algebras we construct a functor from Alg(1, 1) to Set which preserves finite prod...
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Let A and B be two Artin algebras with no semisimple summands. Suppose that there is a stable equivalence α between A and B such that α is induced by exact functors. We present a nice correspondence between indecomposable modules over A and B. As a consequence, we have the following: (1) If A is a self-injective algebra, then so is B; (2) If A and B are finite dimensional algebras over an algeb...
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We define and study familial 2-functors primarily with a view to the development of the 2-categorical approach to operads of [Weber, 2005]. Also included in this paper is a result in which the well-known characterisation of a category as a simplicial set via the Segal condition, is generalised to a result about nice monads on cocomplete categories. Instances of this general result can be found ...
متن کاملRight Modules over Operads and Functors
In the theory of operads we consider generalized symmetric power functors defined by sums of coinvariant modules. One observes classically that the symmetric functor construction provides an isomorphism from the category of symmetric modules to a split subcategory of the category of functors on dgmodules (if dg-modules form our ground category). The purpose of this article is to obtain a simila...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1974
ISSN: 0022-4049
DOI: 10.1016/0022-4049(74)90025-5