# what is the second abstraction lemma in the mother category?

abstraction lemma two

Given a simple map $f:S\to T$ then $f$ can be factored as $f=\beta\circ\rho$ where $\rho$ is the projection $S\to S/{\sim}$ defined as $\rho(s)=[s]$ that is surjective, and $\beta:\frac{S}{\sim}\to T$ defined as $\beta([x])=f(x)$ that is injective