Cohomology vs. Homology

Cohomologynoun

(mathematics) A method of contravariantly associating a family of invariant quotient groups to each algebraic or geometric object of a category, including categories of geometric and algebraic objects.

Homologynoun

A homologous relationship.

Cohomologynoun

(mathematics) A system of quotient groups associated to a topological space.

Homologynoun

(topology) A theory associating a system of groups to each topological space.

Cohomology

In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewed as a method of assigning richer algebraic invariants to a space than homology.

Homologynoun

(algebra) A certain system of groups associated to a chain complex.

Homologynoun

(chemistry) The relationship between the elements in the same group of the periodic table, or between organic compounds in a homologous series.

Homologynoun

(evolutionary theory) A correspondence of structures in two life forms with a common evolutionary origin, such as flippers and hands.

Homologynoun

(genetics) The presence of the same series of bases in related genes.

Homologynoun

The quality of being homologous; correspondence; relation; as, the homologyof similar polygons.

Homologynoun

Correspondence or relation in type of structure in contradistinction to similarity of function; as, the relation in structure between the leg and arm of a man; or that between the arm of a man, the fore leg of a horse, the wing of a bird, and the fin of a fish, all these organs being modifications of one type of structure.

Homologynoun

The correspondence or resemblance of substances belonging to the same type or series; a similarity of composition varying by a small, regular difference, and usually attended by a regular variation in physical properties; as, there is an homology between methane, CH4, ethane, C2H6, propane, C3H8, etc., all members of the paraffin series. In an extended sense, the term is applied to the relation between chemical elements of the same group; as, chlorine, bromine, and iodine are said to be in homology with each other. Cf. Heterology.

Homologynoun

the quality of being similar or corresponding in position or value or structure or function