generalized element

noun

A morphism whose codomain is some specified object.

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Meanings

noungeneralized element (plural generalized elements)

plural generalized elements

  1. category theoryA morphism whose codomain is some specified object.
    1 more example

    Thinking of x#92;in#95;AB as a generalized element, for any f#58;B#92;rightarrowC, we may write f(x) for the composite f#92;circx. In this notation the first domain–codomain axiom reads as follows: for any x#92;in#95;AB and f#58;B#92;rightarrowC there is a well-defined f(x)#92;in#95;AC; that is, at each stage A, f takes A-elements of B to A-elements of C.

    1995, Colin McLarty, Elementary Categories, Elementary Toposes, Oxford University Press, →ISBN, page 17
Cite this entry
APA

generalized element. (n.d.). In WatkinsX Dictionary. Retrieved November 2, 2026, from https://dictionary.watkinsx.com/word/generalized%20element

MLA

“generalized element.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/generalized%20element. Accessed November 2, 2026.

Chicago

WatkinsX Dictionary, s.v. “generalized element,” accessed November 2, 2026, https://dictionary.watkinsx.com/word/generalized%20element.

Source: generalized element on Wiktionary, CC BY-SA 4.0.