solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看5437次
Extension groups between atoms in abelian categories. (arXiv:1810.04306v1 [math.CT])
来源于:arXiv
We introduce the extension groups between atoms in an abelian category. For a
locally noetherian Grothendieck category, the localizing subcategories closed
under injective envelopes are characterized in terms of those extension groups.
We also introduce the virtual dual of the extension groups between atoms to
measure the global dimension of the category. A new topological property of
atom spectra is revealed and it is used to relate the projective dimensions of
atoms with the Krull-Gabriel dimensions. As a byproduct of the topological
observation, we show that there exists a spectral space that is not
homeomorphic to the atom spectrum of any abelian category. 查看全文>>