2015/03/25 by Vincent S. Schlegel, Schlegel, Vincent S.
Arts and Humanities · Mathematics · #18B99 #51K10 #58A03 #Algebraic Geometry and Number Theory #Category Theory (math.CT) #Differential Geometry (math.DG) #FOS: Mathematics #French Literature and Criticism #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1503.07408
openalex publication_date 2015/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that there is a fully faithful embedding of the category of manifolds with corners into the Cahiers topos, one of the premier models for Synthetic Differential Geometry. This embedding is shown to have a number of nice properties, such as preservation of open covers and transverse fibre products. We develop a theory for gluing manifolds with corners in the Cahiers topos. In this setting, the result of gluing together manifolds with corners along a common face is shown to coincide with a pushout along an infinitesimally thickened face. Our theory is designed with a view toward future applications in Field Theory within the context of Synthetic Differential Geometry.