scholarly journals Definable orthogonality classes in accessible categories are small

2015 ◽  
Vol 17 (3) ◽  
pp. 549-589 ◽  
Author(s):  
Joan Bagaria ◽  
Carles Casacuberta ◽  
A.R.D. Mathias ◽  
Jiří Rosický
Keyword(s):  
Accessible Categories

scholarly journals Obstruction theory in action accessible categories

2013 ◽  
Vol 385 ◽  
pp. 27-46 ◽  
Author(s):  
Alan S. Cigoli ◽  
Giuseppe Metere ◽  
Andrea Montoli
Keyword(s):  
Obstruction Theory ◽  
Accessible Categories

scholarly journals A classification of accessible categories

2002 ◽  
Vol 175 (1-3) ◽  
pp. 7-30 ◽  
Author(s):  
Jiřı́ Adámek ◽  
Francis Borceux ◽  
Stephen Lack ◽  
Jiřı́ Rosický
Keyword(s):  
Accessible Categories

scholarly journals PURE-INJECTIVES RELATIVE TO A COTORSION PAIR: APPLICATIONS

2012 ◽  
Vol 55 (1) ◽  
pp. 59-68
Author(s):  
SERGIO ESTRADA ◽  
PEDRO A. GUIL ASENSIO
Keyword(s):  
Classical Theory ◽  
General Class ◽  
Cotorsion Pair ◽  
Coherent Sheaves ◽  
Accessible Categories

AbstractFinitely accessible categories naturally arise in the context of the classical theory of purity. In this paper we generalise the notion of purity for a more general class and introduce techniques to study such classes in terms of indecomposable pure injectives related to a new notion of purity. We apply our results in the study of the class of flat quasi-coherent sheaves on an arbitrary scheme.

scholarly journals Class-locally presentable and class-accessible categories

2012 ◽  
Vol 216 (10) ◽  
pp. 2113-2125 ◽  
Author(s):  
B. Chorny ◽  
J. Rosický
Keyword(s):  
Accessible Categories

scholarly journals METRIC ABSTRACT ELEMENTARY CLASSES AS ACCESSIBLE CATEGORIES

2017 ◽  
Vol 82 (3) ◽  
pp. 1022-1040 ◽  
Author(s):  
M. LIEBERMAN ◽  
J. ROSICKÝ
Keyword(s):  
Abstract Elementary Classes ◽  
Accessible Categories ◽  
Elementary Classes

AbstractWe show that metric abstract elementary classes (mAECs) are, in the sense of [15], coherent accessible categories with directed colimits, with concrete ℵ1-directed colimits and concrete monomorphisms. More broadly, we define a notion of κ-concrete AEC—an AEC-like category in which only the κ-directed colimits need be concrete—and develop the theory of such categories, beginning with a category-theoretic analogue of Shelah’s Presentation Theorem and a proof of the existence of an Ehrenfeucht–Mostowski functor in case the category is large. For mAECs in particular, arguments refining those in [15] yield a proof that any categorical mAEC is μ-d-stable in many cardinals below the categoricity cardinal.

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