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Always Singleton: true there relation: is for an every object and such that for every morphism , there is a morphism , such and that for every other object morphism , there is anonto dagger morphism ,.
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Singleton: Tabulations: there for is every an object such and that , and for morphism every object , there is an objectonto dagger morphism andmaps , , such that and for every object and maps and , and imply .
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Cartesian Power products: sets: for every object , and there is an object and a morphism , there such is that an for object each morphism , and there exists a maps map , such that, such that .
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Tabulations: Function extensionality: for every object and and morphism, there is an object and maps , , such and that , and for two global elements and implies, and imply .
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Power Natural sets: numbers: for there every is an object , there with is maps an object and a morphism , such that for each morphism object , there with exists maps amap and , such there that is a map such that and .
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Function Choice: extensionality: for every object and , and every maps entire dagger epimorphism , and has a section., 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 entire dagger epimorphism has a section.