Algebraic Theories: A Categorical Introduction to General Algebra
Algebraic Theories: A Categorical Introduction to General Algebra
复制标题
代数理论：一般代数的分类介绍
DOI：
10.1017/cbo9780511760754
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发表时间：
2010
影响因子：
1.9
通讯作者：
E. Vitale
中科院分区：
文献类型：
--
作者：
J. Adámek;J. Rosický;E. Vitale
代数理论作为一个概念在 20 世纪 60 年代被引入，是通向一般代数分类观点的基本一步。此外，事实证明它们在数学和计算机科学的各个领域都非常有用。这本精心编写的书基于代数理论系统地介绍了代数，研究生和研究人员都可以理解。它将促进一般代数、范畴论和计算机科学的相互作用。一个中心概念是筛选余极限，即那些与集合中的有限乘积进行交换的概念。作者证明了代数范畴和代数理论之间的对偶性，并讨论了代数理论之间的森田等价。他们还特别关注一排序代数理论和集合上相应的具体代数范畴，以及 S 排序代数理论，这些理论在程序语义中很重要。最后一章致力于代数范畴的有限局域化，这是一个最近的研究领域。
Algebraic theories, introduced as a concept in the 1960s, have been a fundamental step towards a categorical view of general algebra. Moreover, they have proved very useful in various areas of mathematics and computer science. This carefully developed book gives a systematic introduction to algebra based on algebraic theories that is accessible to both graduate students and researchers. It will facilitate interactions of general algebra, category theory and computer science. A central concept is that of sifted colimits - that is, those commuting with finite products in sets. The authors prove the duality between algebraic categories and algebraic theories and discuss Morita equivalence between algebraic theories. They also pay special attention to one-sorted algebraic theories and the corresponding concrete algebraic categories over sets, and to S-sorted algebraic theories, which are important in program semantics. The final chapter is devoted to finitary localizations of algebraic categories, a recent research area.