endomorphisms

An endomorphism is a mathematical function that maps a structure, such as a set or space, to itself while preserving its core properties. In simpler terms, it’s a transformation that takes elements within a system and rearranges, modifies, or reorganizes them without changing the overall structure. For example, rotating or reflecting a geometric shape within the same plane are endomorphisms because the shape’s properties remain intact. These functions help mathematicians understand symmetries and internal relationships within mathematical objects, providing insight into their structure and behavior.