Fiber Bundle - Generalizations

Generalizations

• The notion of a bundle applies to many more categories in mathematics, at the expense of appropriately modifying the local triviality condition.
• In topology, a fibration is a mapping π : E → B which has certain homotopy-theoretic properties in common with fiber bundles. Specifically, under mild technical assumptions a fiber bundle always has the homotopy lifting property or homotopy covering property (see Steenrod 1951, 11.7, for details). This is the defining property of a fibration.