## How distributive are the bad Laver tables?

Suppose that $n\in\omega\setminus\{0\}$. Then define $(S_{n},*)$ to be the algebra where $S_{n}=\{1,…,n\}$ and $*$ is the unique operation on $S_{n}$ where $n*x=x$ $x*1=x+1\,\text{mod}\, n$ and if $y<n$, then $x*(y+1)=(x*y)*(x*1)$. The algebra $(S_{n},*)$ satisfies the self-distributivity law $x*(y*z)=(x*y)*(x*z)$ if and only if $n$ is a power of $2$, and if $n$ is a power of $2$, … Read more

## Poincaré-Birkhoff-Witt theorem for Leibniz algebras

Leibniz algebras can be seen as a non-skew-symmetric generalization of Lie algebras. I have already taken a look at some papers related to Leibniz algebras and extending main results of Lie algebras to Leibniz algebras. Here I want to ask you about the Poincaré-Birkhoff-Witt (PBW) theorem for free Leibniz algebras? Does the PBW theorem allow … Read more

## What is important about Top\mathsf{Top} with regard to models of a homological variety?

Originally from MSE. Consider an algebraic theory whose category of models in Set is homological. This is equivalent to saying that the theory has a unique constant 0 and there exists an n≥1 such that: there are n binary operations αi such that ai(x,x)=0 there is a n+1-ary operation θ with θ(α1(x,y),…,αn(x,y),y)=x Then the category … Read more