книжечку присоветовали

http://www.cs.man.ac.uk/~pt/Practical_Foundations/html/index.html

Practical Foundations of Mathematics

Paul Taylor

heap

 A heap 

(H,t)$(H,t)$ is a nonempty set H$H$ equipped with a ternary operation t:H×H×H→H$t : H \times H \times H\to H$ satisfying the relations

t(b,b,c)=c=t(c,b,b)$$t(b,b,c) = c = t(c,b,b)$$

t(a,b,t(c,d,e))=t(t(a,b,c),d,e)$$t(a,b,t(c,d,e)) = t(t(a,b,c),d,e)$$

More generally, a ternary operation in some variety of algebras satisfying the first pair of equations is called a Mal'cev operation. A Mal’cev operation is called associative if it also satisfies the latter equation (i.e. it makes its domain into a heap).

 

heap to monoid is like affine space to linear space