CLASSIFICATION THEORY FOR ACCESSIBLE CATEGORIES
نویسندگان
چکیده
منابع مشابه
Classification Theory for Accessible Categories
elementary classes (Shelah 1987) form a special case of the former (Lieberman 2011, Beke and JR 2012) and generalize Lκω-elementary classes. Surprisingly, I do not know any abstract elementary class which does not have an Lκω-axiomatization (as an abstract category). With Makkai, we failed to prove that uncountable sets with injective mappings form such an example. It seemed a long time that th...
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For a suitable collection D of small categories, we define the D-accessible categories, generalizing the λ-accessible categories of Lair, Makkai, and Paré; here the λ-accessible categories are seen as the D-accessible categories where D consists of the λ-small categories. A small category C is called D-filtered when C-colimits commute with D-limits in the category of sets. An object of a catego...
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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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[F-S] D. Fremlin and S. Shelah, Pointwise compact and stable sets of measurable functions, manuscript, 1990. [G-G-M-S] N. Ghoussoub, G. Godefroy, B. Maurey, W. Schachermayer, Some topological and geometrical structures in Banach spaces, Mem. Amer. Math. Soc, no. 378, Providence, RI, 1987. [G1 ] G. Godefroy, Parties admissibles d'un espace de Banach. Applications, Ann. Sci. Ecole Norm. Sup 4, (1...
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We give conditions on a finitary endofunctor of a finitely accessible category to admit a final coalgebra. Our conditions always apply to the case of a finitary endofunctor of a locally finitely presentable (l.f.p.) category and they bring an explicit construction of the final coalgebra in this case. On the other hand, there are interesting examples of final coalgebras beyond the realm of l.f.p...
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ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 2016
ISSN: 0022-4812,1943-5886
DOI: 10.1017/jsl.2014.85