If H-* is a generalized homology theory and A a Z-module, we can define the homology with coefficients H-*(-. A), which is linked to the theory H-* by a universal coefficient exact sequence. However, this homology with coefficients is not fonctorial in A. To avoid this ambiguity, we associate with H-* a homology theory (H) over cap (*) that takes values in a certain Abelian category D. Hence we find a new universal coefficient exact sequence, sometimes better than the classical one. (C) 2015 Academie des sciences. Publie par Elsevier Masson SAS. Tous droits reserves.
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机译:如果H- *是广义同源性理论,并且A是Z-模块,则可以定义具有系数H-*(-。A)的同源性,该系数通过通用系数精确序列与理论H- *关联。但是,这种具有系数的同源性在A中并不适用。为避免这种歧义,我们将H- *与上限理论(*)的同源理论(H)关联,该理论采用某个阿贝尔类别D中的值。系数精确的序列,有时比经典序列好。 (C)2015年科学研究院。 Publie par Elsevier Masson SAS。 Tous droits储备。
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