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There is a notion of an anodyne morphism (usually of simplicial sets). This type of morphisms is used, for instance, to establish basic properties of quasicategories. But the name is quite mysterious. Why are such morphisms called anodyne? I checked several sources on simplicial homotopy theory and they all use the word "anodyne" without any explanations. Is there some reason for this particular word to be used for this meaning?

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  • $\begingroup$ I believe the phrase is due to Gabriel and Zisman. $\endgroup$ – Zhen Lin Dec 10 '14 at 20:50
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I don't know who first used the word and why they chose it (probably they never stated explicitly why they chose it anyways), but it seems like an entirely reasonable choice to me when considered in the original context of the simplicial sets as modeling spaces. The word "anodyne" is (rarely) used in ordinary English to mean "inoffensive" or "bland". This seems to me a rather apt description of anodyne morphisms of simplicial sets (aka acyclic cofibrations): they are the morphisms that don't really do anything. They are built by repeatedly attaching simplices to fill in horns, which is "harmless" from a homotopic perspective (it does not change the homotopy type).

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