Courant algebroid relations define spinor and Dirac structure relations, with T-duality inducing spinor relations that generalize twisted cohomology isomorphisms and are compatible with Type II supergravity equations.
Vysoký,Hitchhiker’s Guide to Courant Algebroid Relations,Journal of Geometry and Physics151(2020) 103635 [1910.05347]
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Generalised Complex and Spinor Relations
Courant algebroid relations define spinor and Dirac structure relations, with T-duality inducing spinor relations that generalize twisted cohomology isomorphisms and are compatible with Type II supergravity equations.