Purity and injectivity in accessible categories
نویسندگان
چکیده
منابع مشابه
On Injectivity in Locally Presentable Categories
Classes of objects injective w.r.t. specified morphisms are known to be closed under products and retracts. We prove the converse: a class of objects in a locally presentable category is an injectivity class iff it is closed under products and retracts. This result requires a certain large-cardinal principle. We characterize classes of objects injective w.r.t. a small collection of morphisms: t...
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Continuous lattices were characterised by Mart́ın Escardó as precisely the objects that are Kan-injective w.r.t. a certain class of morphisms. We study Kan-injectivity in general categories enriched in posets. An example: ω-CPO’s are precisely the posets that are Kan-injective w.r.t. the embeddings ω →֒ ω + 1 and 0 →֒ 1. For every class H of morphisms we study the subcategory of all objects Kan-in...
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For any module M over an associative ring R, let σ[M ] denote the smallest Grothendieck subcatgory of Mod-R containingM . If σ[M ] is locally finitely presented the notions of purity and pure injectivity are defined in σ[M ]. In this paper the relationship between these notions and the corresponding notions defined in Mod-R are investigated, and the connection between the resulting Ziegler spec...
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Definition 1.1. A weak factorization system (L,R) in a category K consists of two classes L and R of morphisms of K such that (1) R = L , L = R and (2) any morphism h of K has a factorization h = gf with f ∈ L and g ∈ R. Definition 1.2. A model category is a complete and cocomplete category K together with three classes of morphisms F , C and W called fibrations, cofibrations and weak equivalen...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1998
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(97)00073-x