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In mathematics, homological stability is any of a number of theorems asserting that the group homology of a series of groups G 1 ⊂ G 2 ⊂ ⋯ {\displaystyle G_{1}\subset G_{2}\subset \cdots } is stable, i.e.,
is independent of n when n is large enough. The smallest n such that the maps H i → H i {\displaystyle H_{i}\to H_{i}} is an isomorphism is referred to as the stable range.The concept of homological stability was pioneered by Daniel Quillen whose proof technique has been adapted in various situations.
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