quotientlike
Quotientlike is an informal mathematical descriptor for a construction, object, or map that behaves similarly to a quotient. It typically arises when elements of a structure are identified according to an equivalence relation, partitioning the underlying set or object into equivalence classes and yielding a canonical target that records these identifications.
Formally, if X is a set with an equivalence relation ∼, the quotient X/∼ and the projection π:X→X/∼
Quotientlike constructions occur across areas: in algebra, quotient groups, rings, and modules; in topology, quotient spaces;
Note that quotientlike does not denote a single formal object in every setting. Whether a construction is
See also: quotient set, quotient group, quotient topology, coequalizer, effective epimorphism, congruence relation, quotient type.