Definition 1.4.6 (Arrow category). Let \(C\) be an \(\infty \)-category. We write \[ \Ar (C) \quad := \quad \Fun ([1],C) \] and refer to it as the arrow category of \(C\). Its objects are precisely the morphisms of \(C\). Restriction along the two maps \([0] \to [1]\) defines the source and target functors \[ s := d_1^* = \ev _0\colon \Ar (C) \to C, \qquad t := d_0^* = \ev _1\colon \Ar (C) \to C. \]
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