Learning Functional Programming in Go

Homomorphisms preserve correspondence

Correspondence must be as follows:

• Single-valued: The morphism must at least be a partial function
• Surjective: Each a in A has at least one f(a) in B

Homomorphism is a way to compare two groups for structural similarities. It's a function between two groups that preserve their structure. Suppose we have two groups, G and H. G and H have different group operations. Let's also suppose that G has the group operation ☆ and H has the group operation (♡). Given any two elements in G: a, b ∈ G. And let's suppose  a ☆ b = c. We also have a function f that maps G to H: f: G→ H. The elements a, b, and c are mapped to elements in H. The a variable maps to f(a), b maps to f(b), and c maps to f(c):

• f: a ↦ f(a) ...