Discrete Cocartesian Fibration

A Displayed category ℰ ℰ \mathcal{E} is a discrete cocartesian fibration if every diagram of the form:

X𝑋{X}p⁢(X)𝑝𝑋{{p(X)}}Y𝑌{Y}u𝑢\scriptstyle{u}

has a unique lift ι : X → u ! ⁢ ( X ) : 𝜄 → 𝑋 subscript 𝑢 𝑋 \iota:X\to u_{!}(X) .