BIRS Workshop Lecture Videos
The general linear 2-groupoid del Hoyo, Matias Luis
When working with Lie groupoids, representations up to homotopy arise naturally, and they are useful, for instance, to make sense of the adjoint representation. The idea behind them is to use graded vector bundles and allow non-associativity. We discuss the symmetries of a graded vector bundle and show that, in the 2-term case, they can be regarded as a Lie 2-groupoid. We show that the nerve of a Lie 2-groupoid is a simplicial manifold, and use this construction to realize 2-term representations up to homotopy as pseudo-functors. Based in a joint work with D. Stefani.
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