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I read that the arrow notation $x \rightarrow y$ was invented in the 20th century. Who introduced it?

Each map needs both an explicit domain and an explicit codomain (not just a domain, as in previous formulations of set theory, and not just a codomain, as in type theory). -- Lawvere and Rosebrugh Sets for Mathematics, 2003

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    @alancalvitti: Not usually.2012-05-14

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I found some information HERE

Saunders Mc Lane, in Categories for the working mathematician (Springer-Verlag, 1971, p. 29), says: "The fundamental idea of representing a function by an arrow first appeared in topology about 1940, probably in papers or lectures by W. Hurewicz on relative homotopy groups. (Hurewicz, W.: "On duality theorems," Bull. Am. Math. Soc. 47, 562-563) His initiative immediately attracted the attention of R. H. Fox and N. E. Steenrod, whose ... paper used arrows and (implicitly) functors... The arrow f: : X —> Y rapidly displaced the occasional notation f(X) (subset of ) Y for a function.

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    The question was asked later at MO, and people found occurences predating 1940. https://mathoverflow.net/questions/194377/when-was-the-arrow-notation-for-functions-first-introduced2017-06-25