On injectivity in locally presentable 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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Injectivity with respect to morphisms having λ-presentable domains and codomains is characterized: such injectivity classes are precisely those closed under products, λ-directed colimits, and λ-pure subobjects. This sharpens the result of the first two authors (Trans. Amer. Math. Soc. 336 (1993), 785-804). In contrast, for geometric logic an example is found of a class closed under directed col...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1993
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-1993-1085935-2