Template

From Structures

1 (Name)

(Name)

(Abbrev)

Definition 1

A (Name) is a (brief def), i.e. a structure $\mathbf{A}=\langle A,...\rangle$, where $...$ is an infix binary operation, called the (name), such that

$op$ is (name): $identity$

...

Remark:

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Definition 2

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Definition 3

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Morphisms

Let $\mathbf{A}$ and $\mathbf{B}$ be ... A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a homomorphism:

$h(xy)=h(x)h(y)$

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Basic Results

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Examples

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Properties

Classtype & variety
Equational theory & (un)decidable 
Quasiequational theory & (un)decidable
First-order theory & (un)decidable
Locally finite & yes/no
Residual size & n/...
Congruence distributive & yes/no
Congruence modular & yes/no
Congruence meet-semidistributive & yes/no
Congruence n-permutable & yes/no
Congruence regular & yes/no
Congruence uniform & yes/no
Congruence extension property & yes/no
Definable principal congruences & yes/no
Equationally def. pr. cong. & yes/no
Amalgamation property & yes/no
Strong amalgamation property & yes/no
Epimorphisms are surjective & yes/no

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