nLab
connection

The term connection can mean any of

• connection on a bundle

  • principal connection

    • affine connection

    • Cartan connection

    • Ehresmann connection

    • flat connection

  • meromorphic connection

  • Grothendieck connection

  • simplicial connection

  • connection in noncommutative geometry

• Hurewicz connection

• connection for a differential graded algebra

• p-connection for a smooth map $p$ of smooth schemes or analytic spaces

• connection for a coring

which are all very similar and often special cases of each other, or a sort of dual construction

• hom-connection,

but it can also mean the non-related notions of

• connection on a cubical set and

• connection on a double category,

which are quite different.