Colimits of accessible categories
R. Pare, J. Rosicky
TL;DR
This paper proves that directed colimits of accessible categories and accessible embeddings are themselves accessible, with the result strengthened under the assumption of large strongly compact cardinals.
Contribution
It establishes that directed colimits of accessible categories remain accessible, extending previous results and incorporating large cardinal assumptions for a broader class of colimits.
Findings
Directed colimits of accessible categories are accessible.
Under large cardinal assumptions, all directed colimits of accessible categories are accessible.
The results depend on the existence of arbitrarily large strongly compact cardinals.
Abstract
We show that any directed colimit of acessible categories and accessible full embeddings is accessible and, assuming the existence of arbitrarily large strongly compact cardinals, any directed colimit of acessible categories and accessible embeddings is accessible.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topology and Set Theory · Algebraic structures and combinatorial models