252 research outputs found
Locally class-presentable and class-accessible categories
We generalize the concepts of locally presentable and accessible categories.
Our framework includes such categories as small presheaves over large
categories and ind-categories. This generalization is intended for applications
in the abstract homotopy theory
The accessibility rank of weak equivalences
We study the accessibility properties of trivial cofibrations and weak
equivalences in a combinatorial model category and prove an estimate for the
accessibility rank of weak equivalences. In particular, we show that the class
of weak equivalences between simplicial sets is finitely accessible.Comment: The main result is improved and its proof is simplified. To appear in
Theory and Applications of Categories. 15 page
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