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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMar 7th 2012

    I have added a little bit of discussion to the Idea-section at anodyne morphism, added references, added a mentioning of the dendroidal case, and made anodyne extension redirect to it.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeApr 19th 2016

    I have added the original reference (ch. IV.2 of Grabriel-Zisman) to anodyne extension

    • CommentRowNumber3.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJul 22nd 2022

    Expanded the Idea section:

    The original definition by Gabriel–Zisman (Definition IV.2.1.4 \cite{GabrielZisman67}) defined anodyne extensions as the weak saturation of simplicial horn inclusions.

    More generally, the same definition can be used to talk about the weak saturation of any set S of morphisms in any category. One also talks about anodyne maps or anodyne morphisms.

    If the small object argument is applicable, anodyne maps are precisely maps with a left lifting property with respect to all fibrations, where the latter is defined as morphisms with a right lifting property with respect to S.

    In particular, if S is a set of generating acyclic cofibrations in a model category with applicable small object argument, then anodyne maps are precisely acyclic cofibrations.

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