A talk that I gave:
The (co-)reflective categories of supergravity
Category Theory and Algebra Seminar at Brno (org. Jiří Rosický)
March 12, 2015
(talk notes at super-Cartan geometry)
Abstract. In string theory, the global formulation of the dynamics of super p-branes requires target super spacetimes to be refined to super-stacks (FSS 13). This raises the mathematical problem of classifying the admissible (“anomaly free”) Cartan geometries for such higher supergeometry. In this talk I present a category theoretic analysis which greatly facilitates solving this problem. I discuss how the (higher) topos of super-stacks is stratified by a system of opposing (co-)reflective subcategories that serve to characterize its geometric content. In closing I will give a very brief outlook on how this serves to solve the classification problem.
This diagram shows the system of reflectors and coreflectors on the supergeometric topos. The symbol “$\dashv\,\,$” denotes adjunctions of (co-)reflectors and the symbol “$\vee\,\,$” denotes inclusion of (co-)reflective subcategories. More details are at differential cohomology in a cohesive topos.
The discussion that applies this system of operations to the above problem is at Obstruction theory for parameterized higher WZW terms.
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