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What is a cohomology?

What is a cohomology? Here are some definitions.

Noun
  1. (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.
  2. (mathematics) A system of quotient groups associated to a topological space.
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Examples
He assumes students are familiar with homological algebra, algebraic topology based on different forms, and de Rham cohomology.
We discuss the definition of Picture Lowering and Picture Raising Operators and their relation with the cohomology.
Irregular singularities of linear differential systems in any dimension and over various base fields,and their algebraic de Rham cohomology.
In further papers, published in 1936, he defined cohomology groups for an arbitrary locally compact topological space.
Topology, cohomology, Lie algebras, and knot theory have all become valuable items in the physicist's tool chest.
We will first study equivariant cohomology on some examples.

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