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

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SESSION 33

Parts of an object: Toposes

1.  Parts and inclusions

In the previous session we used the idea of inclusion, which is the basis of truth and logic; now we will consider it in more detail. Logic (in the narrow sense) is primarily about subobjects; the important thing about subobjects is how they are related, and their most basic relationships are given by maps in a certain category.

If X is a given object of a category , then, as we have already explained, we can form another category /X: an object of /X is a map of with codomain X, and ...

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