Synthetic geometry of differential equations: I. Jets and comonad structure

2017/01/23 by Khavkine, Igor, Schreiber, Urs · 1 citation
#51K10 #58A03 #58A20 #Category Theory (math.CT) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1701.06238

Abstract

We give an abstract formulation of the formal theory partial differential equations (PDEs) in synthetic differential geometry, one that would seamlessly generalize the traditional theory to a range of enhanced contexts, such as super-geometry, higher (stacky) differential geometry, or even a combination of both. A motivation for such a level of generality is the eventual goal of solving the open problem of covariant geometric pre-quantization of locally variational field theories, which may include fermions and (higher) gauge fields. (abridged)

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