Class-locally presentable and class-accessible categories
Copyright policy )Class-locally presentable and class-accessible categories
In this paper the authors consider generalisations of accessibility and local presentability for categories. A category is accessible if it has a completeness property and if every object is a colimit in a suitable way of a set of suitable objects. For class-accessibility one allows a proper class of objects rather than a set. Class-local presentability is related to local presentability in a similar way. Class-accessible categories are used in abstract homotopy theory. They are closed under lax limits and have a good theory of weak factorisation systems. Examples of class-accessible categories are given by small presheaves over large categories.
- Masaryk University Czech Republic
- University of Haifa Israel
Homotopy groups, Factorization systems, substructures, quotient structures, congruences, amalgams, abstract homotopy theory, Algebra and Number Theory, class-accessible, weak factorisation systems, Nonabelian homotopical algebra, Accessible and locally presentable categories, class-locally presentable
Homotopy groups, Factorization systems, substructures, quotient structures, congruences, amalgams, abstract homotopy theory, Algebra and Number Theory, class-accessible, weak factorisation systems, Nonabelian homotopical algebra, Accessible and locally presentable categories, class-locally presentable
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