Homological projection is a mathematical term used to represent the projection of a model onto another. It is a process common in manifold theory, algebraic geometry, and topology. The word "homological" refers to the study of topological spaces and their properties. A synonym for homological projection is "topological projection." In differential geometry, it is called "fiber integration," while in algebraic topology, it is referred to as "pushforward." Other synonyms include "homotopic projection" and "homotopic lifting." All these terms share the same meaning and imply the same process but are used in different contexts. Regardless of the synonym used, homological projection plays a significant role in various mathematical fields.