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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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@MichaelJoyce, thanks for markup - still learning Tex –  alancalvitti May 14 '12 at 1:47
Why did you remove the "for functions" on the title? That is what you are asking about, given the quote, right? Arrows are used for a variety of purposes in different settings, so it's important to be clear which setting you are talking about. For example, "$x\to y$" can be used to denote rewriting rules; or implications in the setting of propositional calculus. If you wanted to include things like "functors", then you should add it, not remove all context. –  Arturo Magidin May 14 '12 at 1:51
@ArturoMagidin, I understand your comment but, because - at least today, if not when the notation was introduced - arrows are not necessarily functions (ie, total functional relations). Arrows also refer to functors which carry more information than functions. –  alancalvitti May 14 '12 at 1:55
Then somebody telling you who introduced the notation for material implication would be an acceptable answer? I doubt it sincerely. And by the time the very notion of "functor" was introduced, the arrow was already established as notation for functions, and it was adopted for "functor" as analogy, since a functor is a function between categories. By removing context, you make your question more ambiguous, not better. –  Arturo Magidin May 14 '12 at 1:59
Actually I would be interested in who first used notation for material implication. Sometimes that's written as a double arrow. It's all arrows. Certainly Aristotle didn't use the notation, so I'd like to know any and all applications –  alancalvitti May 14 '12 at 2:02

1 Answer 1

up vote 11 down vote accepted

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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Thank you for the ref –  alancalvitti May 14 '12 at 2:20

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