About: Thinking of x \in_A B as a generalized element, for any f: B \rightarrow C, we may write f(x) for the composite f \circ x. In this notation the first domain–codomain axiom reads as follows: for any x \in_A B and f: B \rightarrow C there is a well-defined f(x) \in_A C; that is, at each stage A, f takes A-elements of B to A-elements of C.     Permalink

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