Cochains are mathematical objects used in the field of algebraic topology, particularly in the study of chain complexes. They are functions that assign values to the chains of a topological space, allowing for the analysis of its structure. Essentially, cochains help in understanding how different parts of a space relate to each other through algebraic means. In more technical terms, a cochain is a mapping from a set of simplices (basic building blocks of a space) to a coefficient group, such as the integers or real numbers. This mapping can be used to define cohomology, which provides important insights into the properties of spaces, such as their connectivity and holes.