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Conceptual Mathematics, Second Edition by Stephen H. Schanuel, F. William Lawvere

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ARTICLE VI

The contravariant parts functor

1.  Parts and stable conditions

The existence of map objects is already a very powerful (and very useful) property that a category might have. But even stronger properties are realizable; for example, the categories /X might themselves have map objects. The concept of part (or subobject) in might be representable ...

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