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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====
		+
		+
		+