# Differences

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conjugative_binars [2018/08/04 18:39] (current)
jipsen created
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+=====Conjugative binars=====
+
+Abbreviation: **ConBin**
+====Definition====
+A \emph{conjugative binar} is a [[binar]] $\mathbf{A}=\langle A,\cdot\rangle$ such that
+
+$\cdot$ is conjugative: $\exists w, \ x\cdot w=y \iff \exists w, \ w\cdot x=y$.
+
+==Morphisms==
+Let $\mathbf{A}$ and $\mathbf{B}$ be commutative binars. A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a homomorphism:
+
+$h(x\cdot y)=h(x)\cdot h(y)$
+
+====Examples====
+Example 1:
+
+====Basic results====
+
+
+====Properties====
+^[[Classtype]]  |  first-order |
+^[[Equational theory]]  |   |
+^[[Quasiequational theory]]  |   |
+^[[First-order theory]]  |   |
+^[[Locally finite]]  |  no |
+^[[Residual size]]  |   |
+^[[Congruence distributive]]  |  no |
+^[[Congruence modular]]  |  no |
+^[[Congruence n-permutable]]  |  no |
+^[[Congruence regular]]  |  no |
+^[[Congruence uniform]]  |  no |
+^[[Congruence extension property]]  |   |
+^[[Definable principal congruences]]  |   |
+^[[Equationally def. pr. cong.]]  |   |
+^[[Amalgamation property]]  |   |
+^[[Strong amalgamation property]]  |   |
+^[[Epimorphisms are surjective]]  |   |
+
+====Finite members====
+
+^n  ^  # of algebras^
+|1  |  1|
+|2  |  4|
+|3  |  215|
+
+====Subclasses====
+[[Commutative binars]]
+
+[[Conjugative semigroups]]
+
+====Superclasses====
+[[Binars]]
+
+====References====
+
+
+