homology

1. The relationship of being homologous; a homologous relationship.

   (countable, uncountable)Specifically, such relationship in the context of the geometry of perspective.

2. (countable, uncountable)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.

   If the homology centre lies on the homology axis, the homology is said to be singular or parabolic; otherwise, it is called non-singular or hyperbolic.

   Homologie

3. (countable, uncountable)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.

   Homologie

4. (countable, uncountable)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.

   Because of their connection with both homology and cohomology, chain complexes are an important topic of study in homological algebra.

   Homologie

5. (countable, uncountable)The relationship, between elements, of being in the same group of the periodic table.

   Homologie

6. (countable, uncountable)The relationship, between organic compounds, of being in the same homologous series.

   Homologie

7. (countable, uncountable)The relationship, between characteristics or behaviours, of having a shared evolutionary or developmental origin;

8. The relationship, between characteristics or behaviours, of having a shared evolutionary or developmental origin; (evolutionary theory) specifically, a correspondence between structures in separate life forms having a common evolutionary origin, such as that between mammalian flippers and hands.

   (countable, uncountable)Specifically, a correspondence between structures in separate life forms having a common evolutionary origin, such as that between mammalian flippers and hands.

9. The relationship of being homologous; a homologous relationship.

   (countable, uncountable)The presence of the same series of bases in different but related genes.

   Homologie

10. (countable, uncountable)The relationship, between temporally separated human beliefs, practices or artefacts, of possessing shared characteristics attributed to genetic or historical links to a common ancestor.

    Homologie

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