Exactness refers to a property of a sequence of algebraic structures, such as groups or modules, where the image of one morphism equals the kernel of the next. This condition ensures that information is preserved and not lost in the sequence, which is crucial for establishing relationships among cohomological and homological groups. Understanding exactness helps analyze how different spaces or structures relate through induced cohomomorphisms, relative homology, and various sequences like Mayer-Vietoris or duality principles.
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