Composition of matrix products and categorical equivalence
Composition of matrix products and categorical equivalence
复制标题
矩阵乘积的组成和分类等价
DOI：
10.1007/s00012-013-0235-2
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发表时间：
2013
影响因子：
0.6
通讯作者：
Shohei Izawa
中科院分区：
文献类型：
--
作者：
K. Fujiwara;T. Katayama;S-i. M. Nomura;Shohei Izawa
首先，我们证明了两个有限代数是范畴等价的当且仅当它们的非冗余不可加细覆盖的矩阵积是同构的。其次，我们的特点是家庭的不可约代数，使存在一个代数，其邻域在一个不可加细覆盖同构于各自的不可约代数在给定的家庭。最后，我们通过构造实例来展示两个事实。第一个是有一族不可约代数，使得有许多代数结构，其在不可冗余不可加细覆盖中的邻域同构于给定族中的相应不可约代数。第二个例子是一个代数，使得一个非冗余不可加细覆盖的矩阵积大于给定的代数。
First, we prove two finite algebras are categorically equivalent if and only if the matrix products of their irredundant non-refinable covers are isomorphic. Second, we characterize families of irreducible algebras such that there exists an algebra whose neighbourhoods in an irredundant non-refinable cover are isomorphic to the respective irreducible algebra in the given family. Finally, we exhibit two facts by constructing examples. The first one is that there is a family of irreducible algebras such that there are many algebraic structures whose neighbourhoods in an irredundant non-refinable cover are isomorphic to the respective irreducible algebra in the given family. The second example is an algebra such that the matrix product of an irredundant non-refinable cover is bigger than the given algebra.