2023/05/02 by Bár, Filip
#18C10 (Primary) 18B99 #18C35 #18F10 (Secondary) #18F40 #51K10 #Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2305.01357
Categories of models of algebraic theories have good categorical properties except for gluing. Building upon insights and examples from Synthetic Differential Geometry, we introduce a generalisation of models of algebraic theories to infinitesimal models. We demonstrate that the category of infinitesimal models retains most of the good categorical properties, but with a stark improvement in the behaviour of gluing. This makes infinitesimal models an interesting natural construction with the ability to interpolate between algebra and geometry.