Category of coverings

Equivalence of coverings criterion

Let and be connected and locally path-connected coverings. Then and are equivalent iff , homotopy i.e. iff they have the same characteristic subgroup.

Proof

By discussion in Category of coverings with basepoint, if there exists a unique and . Moreover, the identities and are the only morphisms in and respectively. Therefore and , hence and are equivalent.

---

tidy | en | sembr