Connections on principal Lie groupoid bundles are defined through an action up to homotopy, yielding an Atiyah sequence of diffeological groupoids that such connections split.
Equiva riant cohomology for differentiable stacks
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Connections on a principal Lie groupoid bundle and representations up to homotopy
Connections on principal Lie groupoid bundles are defined through an action up to homotopy, yielding an Atiyah sequence of diffeological groupoids that such connections split.