The generalization of the notion of flat connection from differential geometry to higher differential geometry and generally to higher geometry.
Given a cohesive (∞,1)-topos with shape modality and flat modality , a flat -connection an an object with coefficients in an object is a morphism
or equivalently a morphism
This is also sometimes called a local system on with coefficients in , or a cocycle in nonabelian cohomology of with constant coefficients .
For the delooping of an ∞-group, flat -connections with coefficients in are a special case of -principal ∞-connections.
For more see at structures in a cohesive (∞,1)-topos – flat ∞-connections.
Last revised on May 26, 2022 at 02:18:09. See the history of this page for a list of all contributions to it.