Inner Fibration
Inner fibrations impose the inner-horn lifting condition relative to a map of simplicial sets. Compare left, right, and inner fibrations, then specialize the base to a point to recover the quasicategory condition.
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Simplicial Set · Kan Complex · Higher Categories and the Topos Bridge
Where to read
Start here: Higher Topos Theory
Jacob Lurie · Book · English · Free full text
Chapter 2, Definition 2.0.0.3 (Joyal), printed p. 53: relative left-, right-, and inner-horn lifting conditions
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Category Theory in the library · Preparation and skip guidance