This is a subentry of a reading guide to HTT.
Definition 4.1: cofinal arrow Proposition 4.1.3.1: Cofinal arrows preserve colimits
Theorem 4.2.4.1: relation of -categorial colimits and homotopy colimits in simplicially enriched categories.
Proposition 4.2.4.4 (and Corollary 4.2.4.7)in a simplicial model category every homotopy coherent diagram is equivalent to a commutative diagram
construction of colimits from basic diagrams