Transitive Group Action

A Group Action $\cdot:G\times X\to X$ is transitive if for every $x,y:X$, there exists some $g:G$ such that $g\cdot x=y$. Equivalently, a group action is transitive if the Shear Map $\langle\cdot,\pi_{2}\rangle:G\times X\to X\times X$ is an Epimorphism.