@article{Quirin_Tabareau_2016, title={Lawvere-Tierney sheafification in Homotopy Type Theory}, volume={9}, url={https://jfr.unibo.it/article/view/6232}, DOI={10.6092/issn.1972-5787/6232}, abstractNote={Sheafification is a popular tool in topos theory which allows to extend the internal logic of a topos with new principles. One of its most famous applications is the possibility to transform a topos into a boolean topos using the dense topology, which corresponds in essence to Gödel’s double negation translation. The same construction has not been developed in Martin-Löf type theory because of a mismatch between topos theory and type theory. This mismatched has been fixed recently by considering homotopy type theory, an extension of Martin-Löf type theory with new principles inspired by category theory and homotopy theory, and which corresponds closely to higher toposes. In this paper, we give a computer-checked construction of Lawvere-Tierney sheafification in homotopy type theory.}, number={2}, journal={Journal of Formalized Reasoning}, author={Quirin, Kevin and Tabareau, Nicolas}, year={2016}, month={Jan.}, pages={131–161} }