noun

• The relationship of being homologous; a homologous relationship;
• (geometry, projective geometry) An automorphism of the projective plane (representing a perspective projection) that leaves all the points of some straight line (the homology axis) fixed and maps all the lines through some single point (the homology centre) onto themselves.
• (topology, algebraic topology) A general way of associating a sequence of algebraic objects, such as abelian groups or modules, to a sequence of topological spaces; also used attributively: see Usage notes below.
• (algebra) Given a chain complex {Gₙ} and its associated set of homomorphisms {Hₙ}, the rule which explains how each Hₙ maps Gₙ into the kernel of Gₙ₊₁.
• (chemistry) The relationship, between elements, of being in the same group of the periodic table.
• (organic chemistry) The relationship, between organic compounds, of being in the same homologous series.
• (biology, psychology) The relationship, between characteristics or behaviours, of having a shared evolutionary or developmental origin;
• (genetics) The presence of the same series of bases in different but related genes.
• (anthropology) The relationship, between temporally separated human beliefs, practices or artefacts, of possessing shared characteristics attributed to genetic or historical links to a common ancestor.