nLab
principal connection

Idea

The term principal connection is synonymous to connection on a principal bundle .

The most well known examples are affine connections.

Given a $G$-representation $V$ and a $G$-principal connection, it induces a connection on the corresponding $V$-associated bundle.

Related concepts

• connection on a bundle

  • parallel transport, holonomy

• principal connection

  • affine connection, Levi-Civita connection Cartan connection

• connection on a 2-bundle

• connection on an infinity-bundle

  • higher parallel transport

higher Atiyah groupoid

higher Atiyah groupoid:	standard higher Atiyah groupoid	higher Courant groupoid	groupoid version of quantomorphism n-group
coefficient for cohomology:	$B𝔾$	$B(B{𝔾}_{\mathrm{conn}})$	$B{𝔾}_{\mathrm{conn}}$
type of fiber ∞-bundle:	principal ∞-bundle	principal ∞-connection without top-degree connection form	principal ∞-connection