TY - JOUR
AU - Quirin, Kevin
AU - Tabareau, Nicolas
PY - 2016/01/01
Y2 - 2023/02/08
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 -