generalized element

English

Noun

generalized element (plural generalized elements)

1. (category theory) A morphism whose codomain is some specified object.
   • 1995, Colin McLarty, Elementary Categories, Elementary Toposes, Oxford University Press, →ISBN, page 17:

     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.

Hyponyms

• generic element