Implication Details
Claim: A category is locally finitely multi-presentable if and only if it is finitely accessible and is multi-cocomplete.
Proof: This follows from one of equivalent formulations of locally finitely multi-presentable categories.
Claim: A category is locally finitely multi-presentable if and only if it is finitely accessible and is multi-cocomplete.
Proof: This follows from one of equivalent formulations of locally finitely multi-presentable categories.