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Groupoids

Abbreviation: BinOp

Definition

A groupoid is a structure $\mathbf{A}=\langle A,\cdot\rangle$ where $\cdot$ is any binary operation on $A$.

Morphisms

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

$h(x\cdot y)=h(x)\cdot h(y)$

Example 1:

Properties

Classtype variety decidable undecidable no unbounded no no no no no no no no yes yes yes

Finite members

$\begin{array}{lr} f(1)= &1\\ f(2)= &10\\ f(3)= &3330\\ f(4)= &178981952\\ f(5)= &2483527537094825\\ f(6)= &14325590003318891522275680\\ f(7)= &50976900301814584087291487087214170039\\ f(8)= &155682086691137947272042502251643461917498835481022016 \end{array}$