HOW ALGEBRAIC IS ALGEBRA
HOW ALGEBRAIC IS ALGEBRA
复制标题
代数是怎样的
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
J. Rosický
中科院分区：
文献类型：
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作者：
J. Adámek;F. Lawvere;J. Rosický
[摘要]有限品种的2类VAR在CAT上不是品种性的。引入代数正合范畴的概念，证明了所有代数正合范畴的2-范畴ALG是VAR w. r. t的一个方程船体.所有操作都有等级。每个代数正合范畴K是完备的、正合的，并且有滤余极限，滤余极限（a）与有限极限可换，滤余极限（B）分布在乘积上;此外，滤余极限（c）K中的正则满态是乘积稳定的。目前尚不清楚（a）-（c）是否表征代数精确性。VAR方程的船体。还讨论了所有操作。
Y ∗ ABSTRACT. The 2-category VAR of finitary varieties is not varietal over CAT . We introduce the concept of an algebraically exact category and prove that the 2-category ALG of all algebraically exact categories is an equational hull of VAR w.r.t. all op- erations with rank. Every algebraically exact category K is complete, exact, and has filtered colimits which (a) commute with finite limits and (b) distribute over products; besides (c) regular epimorphisms in K are product-stable. It is not known whether (a) - (c) characterize algebraic exactness. An equational hull of VAR w.r.t. all operations is also discussed.