TY - JOUR AU - Quirin, Kevin AU - Tabareau, Nicolas PY - 2016/01/01 Y2 - 2024/03/28 TI - Lawvere-Tierney sheafification in Homotopy Type Theory JF - Journal of Formalized Reasoning JA - JFR VL - 9 IS - 2 SE - Articles DO - 10.6092/issn.1972-5787/6232 UR - https://jfr.unibo.it/article/view/6232 SP - 131-161 AB - 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. ER -