The SQL Join can be thought of as the follows:

• A join is a lookup
• A join is a nested loop over rows
• A join is a nested loop over columns
• A join is compatible alternate realities
• A join is flatMap
• A join is the solution to the N+1 problem
• A join is paths through a graph
• A join is a minimal model
• A join is typechecking
• A join is an operation in the Set monad
• A join is the biggest acceptable relation
• A join is a…join
• A join is a ring product

These are nice ways to illustrate a non-trivial algebraic structure.