homology category
A homology category is a mathematical concept that generalizes the notion of homology from algebraic topology to other areas of mathematics. It is a category equipped with a family of functors that assign to each object in the category a sequence of abelian groups, called homology groups, and to each morphism a sequence of morphisms between the corresponding homology groups, satisfying certain axioms. These functors capture the underlying structure and relationships between objects in the category through algebraic invariants, providing a way to study and compare objects within the category.
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