A homotopy-coherent calculus of lax matrices

Abstract

This thesis consists of two chapters, together with two supporting appendices. The first chapter describes the construction of a homotopy-coherent calculus of lax matrices. The second chapter gives a construction of a lax monoidal structure on the functor implementing pull-push of local systems along spans of infinity-groupoids. The first appendix shows that the notion of internal left Kan extension can be captured by horn filling conditions, and the second proves a formula for reflective localization in terms of spans.