Sizes and filtrations in accessible categories
Autor: | Sebastien Vasey, Jiří Rosický, Michael Lieberman |
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Rok vydání: | 2020 |
Předmět: |
Discrete mathematics
General Mathematics 010102 general mathematics Accessible category Object (grammar) 0102 computer and information sciences 01 natural sciences Mathematics::Logic Cardinality 010201 computation theory & mathematics Mathematics::Category Theory Retract 0101 mathematics Algebra over a field Mathematics |
Zdroj: | Israel Journal of Mathematics. 238:243-278 |
ISSN: | 1565-8511 0021-2172 |
DOI: | 10.1007/s11856-020-2018-8 |
Popis: | Accessible categories admit a purely category-theoretic replacement for cardinality: the internal size. Generalizing results and methods from [LRV19b], we examine set-theoretic problems related to internal sizes and prove several Lowenheim–Skolem theorems for accessible categories. For example, assuming the singular cardinal hypothesis, we show that a large accessible category has an object in all internal sizes of high-enough co-finality. We also prove that accessible categories with directed colimits have filtrations: any object of sufficiently high internal size is (the retract of) a colimit of a chain of strictly smaller objects. |
Databáze: | OpenAIRE |
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