Resolution (algebra)
In mathematics, particularly in abstract algebra and homological algebra, a resolution (or left resolution; dually a coresolution or right resolution) is an exact sequence of modules (or, more generally, of objects in an abelian category), which is used to describe the structure of a specific module or object of this category.
Generally, the objects in the sequence are restricted to have some property P (for example to be free). Thus one speaks of a P resolution: for example, a flat resolution, a free resolution, an injective resolution, a projective resolution. The sequence is supposed to be infinite to the left (to the right for a coresolution). However, a finite resolution is one where only finitely many of the objects in the sequence are non-zero.
Read more about Resolution (algebra): Resolutions in Abelian Categories, Acyclic Resolution, See Also
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