cocompletion

English

co- +‎ completion

cocompletion (plural cocompletions)

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

单词	cocompletion
释义	cocompletion English Etymology co- +‎ completion Noun cocompletion (plural cocompletions) (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: We show that ${\\displaystyle j}$ satisfies this condition if and only if ${\\displaystyle j}$ presents ${\\displaystyle {\\mathcal {V}}}$ as a free cocompletion of ${\\displaystyle {\\mathcal {J}}}$ with respect to the weights for left Kan extensions along ${\\displaystyle j}$ , and so we call such systems of arities eleutheric.
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