Localisations of locally presentable categories II
نویسندگان
چکیده
منابع مشابه
Homotopy Locally Presentable Enriched Categories
We develop a homotopy theory of categories enriched in a monoidal model category V. In particular, we deal with homotopy weighted limits and colimits, and homotopy local presentability. The main result, which was known for simplicially-enriched categories, links homotopy locally presentable V-categories with combinatorial model V-categories, in the case where all objects of V are cofibrant.
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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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We show that subobjects and quotients respectively of any object K in a locally finitely presentable category form an algebraic lattice. The same holds for the internal equivalence relations on K. In fact, these results turn out to be—at least in the case of subobjects—nothing but simple consequences of well known closure properties of the classes of locally finitely presentable categories and ...
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We prove that any full subcategory of a locally finitely presentable (l.f.p.) category having small limits and filtered colimits preserved by the inclusion functor is itself l.f.p. Here "full" may be weakened to "full with respect to isomorphisms." Further, we characterize those left exact functors T. C —» D between small categories with finite limits for which the functor /*: LEX(D,Set) —> LEX...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1990
ISSN: 0022-4049
DOI: 10.1016/0022-4049(90)90068-s