Sentence:  Choosing for U the operation of closure, regularization or relative completion, we obtain from a given <WSD>functor</WSD> \mathcal{F}\in\mathcal{JF} the <WSD>functors</WSD> / :: \overline{F} : \overrightarrow{X} \rightarrow \overline{F(\overrightarrow{X})}, F^0 : \overrightarrow{X}\rightarrow F(\overrightarrow{X})^0, F^c : \overrightarrow{X} \rightarrow F(\overrightarrow{X})^c. 
Meaning of the word marked with <WSD> tags:  A category homomorphism; a morphism from a source category to a target category which maps objects to objects and arrows to arrows, in such a way as to preserve domains and codomains (of the arrows) as well as composition and identities.