Jónsson's lemma

Jónsson's lemma is a concept in algebra and lattice theory that explains how certain properties of complex systems, like algebraic structures, can be understood through smaller, more manageable pieces called substructures. Specifically, it states that if a large structure is built in a way that covers all possible sub-structures (called a "Jónsson chain"), then any homomorphism (structure-preserving map) from a smaller piece to another structure can be "lifted" or extended to the entire large structure. This helps mathematicians analyze and understand the properties of complex systems by examining their simpler components.