The more common morphisms are:

**1. Homomorphism** (Similarity between 2 different structures) 同态

Analogy: Similar triangles of 2 different triangles.

**2. Isomorphism** (Sameness between 2 different structures) 同构

Analogy: Congruence of 2 different triangles

Example: 2 objects are *identical* up to an *isomorphism.*

**3. Endomorphism** (Similar structure of self) = {Self + Homomorphism} 自同态

Analogy: A triangle and its image in a magnifying glass.

** 4. Automorphism** (Sameness structure of self) = {Self + Isomorphism} 自同构

Analogy: A triangle and its image in a mirror; or

A triangle and its rotated (clock-wise or anti-clock-wise), or reflected (flip-over) self.

** 5. Monomorphism 单同态 = Injective + Homomorphism **

** 6. Epimorphism 满同态 = Surjective + Homomorphism **