M. Hyland | Searcharxiv

arXiv2024

Monoidal bicategories, differential linear logic, and analytic functors

We develop further the theory of monoidal bicategories by introducing and studying bicategorical counterparts of the notions of a linear exponential comonad, as considered in the study of linear logic, and of a codereliction transformation, introduced to study differential linear logic via differential categories. As an application, we extend the differential calculus of Joyal's analytic functors to analytic functors between presheaf categories, just as ordinary calculus extends from a single variable to many variables.

math.CT↗

arXiv2017

The 67P/Churyumov-Gerasimenko observation campaign in support of the Rosetta mission

We present a summary of the campaign of remote observations that supported the European Space Agency's Rosetta mission. Telescopes across the globe (and in space) followed comet 67P/Churyumov-Gerasimenko from before Rosetta's arrival until nearly the end of mission in September 2016. These provided essential data for mission planning, large-scale context information for the coma and tails beyond the spacecraft, and a way to directly compare 67P with other comets. The observations revealed 67P to be a relatively `well behaved' comet, typical of Jupiter family comets and with activity patterns that repeat from orbit-to-orbit. Comparison between this large collection of telescopic observations and the in situ results from Rosetta will allow us to better understand comet coma chemistry and structure. This work is just beginning as the mission ends -- in this paper we present a summary of the ground-based observations and early results, and point to many questions that will be addressed in future studies.

astro-ph.EP↗