A Cartan -Ehresmann -connection is what is obtained from an Ehresmann ∞-connection after applying the ∞-Lie differentiation functor that sends the Ehresmann ∞-connection diagram of ∞-Lie groupoids
to the diagram
of ∞-Lie algebroids that encodes a system of ∞-Lie algebroid valued differential forms.
The corresponding diagram of Chevalley-Eilenberg algebras is
Such a diagram of ∞-Lie algebroid valued differential forms on a principal ∞-bundle we call a Cartan-Ehresmann -connection . It appears in this form in SaScStI.
Revised on October 20, 2009 10:42:22
by Urs Schreiber