Here, we introduce and apply non-Abelian tensor Berry connections to topological phases in multi-band systems. These gauge behave as antisymmetric fields momentum space naturally generalize Abelian ordinary (vector) connections. We build these novel from momentum-space Higgs fields, which emerge the degenerate band structure of degenerate-band models. Firstly, show that conventional invariants ...

We introduce and develop the notion of scalar extension for abelian categories. Given a field extension F /F , to every F -linear abelian category A satisfying a suitable finiteness condition we associate an F -linear abelian category A ⊗F F ′ and an exact F -linear functor t : A → A ⊗F F . This functor is universal among F -linear right exact functors with target an F -linear abelian category....