Relational Sets and Categorical Equivalence of Algebras
Relational Sets and Categorical Equivalence of Algebras
复制标题
关系集和代数的范畴等价
DOI：
10.1142/s0218196797000253
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
L. Zádori
中科院分区：
文献类型：
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作者：
L. Zádori
我们研究的关系品种，即类的关系集（重置）的相同类型的产品和收缩的形成下关闭。不可约重置和重置表示的概念与偏序集的概念类似。我们给出了有限不可约重置的一个特征。我们表明，每一个有限的复位有一个代表性的最小复位是某些杰出的不可约收缩。结果表明，最小重置表示在某种意义上是重置的所有表示中最小的一个。我们证明了非同构有限不可约重置产生不同的关系品种。我们通过代数的某些重置的乘积和收缩刻画了代数的范畴等价。在有限的情况下，特征涉及最小的重置。给出的例子来证明一般定理如何适用于特定的代数和重置。
We study relation varieties, i.e. classes of relational sets (resets) of the same type that are closed under the formation of products and retracts. The notions of an irreducible reset and a representation of a reset are defined similarly to the ones for partially ordered sets. We give a characterization of finite irreducible resets. We show that every finite reset has a representation by minimal resets which are certain distinguished irreducible retracts. It turns out that a representation by minimal resets is a smallest one in some sense among all representations of a reset. We prove that non-isomorphic finite irreducible resets generate different relation varieties. We characterize categorical equivalence of algebras via product and retract of certain resets associated with the algebras. In the finite case the characterization involves minimal resets. Examples are given to demonstrate how the general theorems work for particular algebras and resets.