Handbook of Categorical Algebra: Bibliography
Handbook of Categorical Algebra: Bibliography
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分类代数手册：参考书目
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
F. Borceux
中科院分区：
文献类型：
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作者：
F. Borceux
《范畴代数手册》的目的是，用三卷的篇幅，详细介绍理想情况下，每个从事范畴论研究的人都应该知道的东西，不管他们选择的是什么具体的研究课题。本书还计划作为该领域的专家和所有使用范畴论作为工具的人的参考书。第3卷从区域理论的基本方面开始，在第2章中继续研究区域和拓扑空间上的结构，以及它们的各种等价表示：函子、线性映射或w集。然后，将这种情况推广到场地上的轮轴情况，并引入相应的格罗滕迪克拓扑的概念。第四章通过证明所有连贯理论的分类拓扑的存在，将格罗滕迪克拓扑理论与可及范畴和草图理论联系起来。
The Handbook of Categorical Algebra is intended to give, in three volumes, a rather detailed account of what, ideally, everybody working in category theory should know, whatever the specific topic of research they have chosen. The book is planned also to serve as a reference book for both specialists in the field and all those using category theory as a tool. Volume 3 begins with the essential aspects of the theory of locales, proceeding to a study in chapter 2 of the sheaves on a locale and on a topological space, in their various equivalent presentations: functors, etale maps or W-sets. Next, this situation is generalized to the case of sheaves on a site and the corresponding notion of Grothendieck topos is introduced. Chapter 4 relates the theory of Grothendieck toposes with that of accessible categories and sketches, by proving the existence of a classifying topos for all coherent theories.