nLab
ETCR
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Idea
A model of the Elementary Theory of the Category of Relations (ETCR) is the dagger 2-poset whose category of maps is a model of ETCS.
Definition
A model of ETCR is a dagger 2-poset such that:
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Singleton: there is an object such that for every morphism , , and for every object there is an onto morphism .
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Tabulations: for every object and and morphism , there is an object and jointly monic maps , , such that .
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Power sets: for every object , there is an object and a morphism such that for each morphism , there exists a map such that .
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Function extensionality: for every object and and maps , and , implies .
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Natural numbers: there is an object with maps and , such that for each object with maps and , there is a map such that and .
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Choice: for every object and , every epic map has a section.
See also
Last revised on May 14, 2022 at 00:37:48.
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