A kind of fibration in the context of homotopy theory.

A Kan fibration $p : E \to B$ is called a minimal Kan fibration if for all cells $x,y : \Delta[n] \to E$ the condition $p(x) = p(y)$ and $\partial_i x = \partial_i y$ implies for all $k$ that $\partial_k x = \partial_k y$.

(…)

A useful (if old) survey article which contains a summary of early results on these is: