Mapping preserving vertices and edges.

Equivalence class under structure-preserving map.

(category theory) A natural transformation whose every component is an isomorphism.

Bijective linear map between spaces.

(algebra) A ring homomorphism which is also a bijection.

In abstract algebra, a group isomorphism is a function between two groups that sets up a bijection between the elements of the groups in a way that respects the given group operations.

In mathematics, specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship among quotients, homomorphisms, and subobjects.