Expanded the Idea section:

The original definition by Gabrielâ€“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.

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

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.