Loops and suspensions in a pointed ∞-category

Definition 4.1.6 (Loop and suspension). Let \(C\) be a pointed \(\infty \)-category. If \(C\) admits fibers, we define the loop object of \(X\in C\) by \[ \Omega X:=\fib (0\to X). \] If \(C\) admits cofibers, we define its suspension by \[ \Sigma X:=\cofib (X\to 0). \]