cocompletion

English

Etymology

co- +‎ completion

Noun

cocompletion (plural cocompletions)

1. (mathematics) A full embedding whose image is a cocomplete category and for which every functor with a cocomplete image has an extension to a cocontinuous functor that is unique up to natural isomorphism.
   • 2015, Rory B. B. Lucyshyn-Wright, “Enriched algebraic theories and monads for a system of arities”, in arXiv‎^[1]:

     We show that $j$ satisfies this condition if and only if $j$ presents ${\mathcal {V}}$ as a free cocompletion of ${\mathcal {J}}$ with respect to the weights for left Kan extensions along $j$, and so we call such systems of arities eleutheric.