I'm just looking for the right words to use to talk about something like the "bijective correspondence" between the class of groups defined as pairs and the class of groups defined as 4-tuples. I'm talking about the "map" ##(G,\star,i,e)\mapsto (G,\star)##. It seems to me that it shouldn't be called "map", "function", "bijection" or anything like that, since its "domain" and "codomain" aren't sets. So is there something we can call it?(adsbygoogle = window.adsbygoogle || []).push({});

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# (Terminology) bijective correspondence between proper classes?

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