Implication Details
Assumptions: locally presentable
Conclusions: cocomplete, complete, generating set, locally essentially small, well-copowered, well-powered
Reason: For locally essential smallness, see the proof of Prop. 2.1.5 in Makkai-Pare. For the other non-trivial conclusions see Adamek-Rosicky, Thm. 1.20, Cor. 1.28, Rem. 1.56, Thm. 1.58.