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 ...