Definition 14.30.1. A map $X \to Y$ of simplicial sets is called a trivial Kan fibration if $X_0 \to Y_0$ is surjective and for all $n \geq 1$ and any commutative solid diagram

$\xymatrix{ \partial \Delta [n] \ar[r] \ar[d] & X \ar[d] \\ \Delta [n] \ar[r] \ar@{-->}[ru] & Y }$

a dotted arrow exists making the diagram commute.

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