Definition 6.59.
The Postnikov-completion of a presentable category \(C\) is defined as the limit
\[\widehat{C}\quad := \quad \lim_n C_{\leq n}.\]
Here the transition functor \(C_{\leq n+1}\to C_{\leq n}\) is \(\tau_n\), and the limit is formed in presentable categories and colimit-preserving functors. We say that \(C\) is Postnikov-complete if the canonical functor \(\tau_*\colon C \to \widehat{C}, X \mapsto (\tau_n X)_n\) is an equivalence.