\(L\)-groupoids: Algebraic and topological properties of special groupoids (Q1866615)

An \(L\)-groupoid is a set \(X\) with a binary operation \(\cdot\) satisfying the identities \(x\cdot x=x\) and \((x\cdot y)\cdot z=x\cdot z\). An \(L\)-groupoid is a generalization of a rectangular band (in the paper a rectangular band is called flexibel). The topological and/or differentiable versions of \(L\)-groupoids are defined. The basic properties of \(L\)-groupoids are proven (most of them can be found in any standard semigroup monograph).