Prove every onto homomorphism is a co-equalizer for a pair of homomorphisms Let $K$ be the collection of algebras of similar type with all the homomorphisms between them. Show that every onto homomorphism is a coequalizer of a pair of homomorphism.
Preliminaries 
Onto Homomorphism : self explanatory
Coequalizer : is a pair $(C, s)$ where $C$ is an algebra and $s$ is a mapping such that for two homomorphisms $h,k : A \to B$ we have $s : B \to C$ such that $sh = sk$ and given any other algebra $D$ and $t : B \to D$ with $th = tk$ there exists unique $r : C \to D$ with $rs = t$
In a previous post I defined $C = B/\theta$ where $\theta $ is the equivalence relation defined by $h(a) = k(a), \forall a \in A$
I am not seeing how I can get the appropriate connection here.  

Hint. Consider $A = \{(b_1, b_2) \in B \times B \mid s(b_1) = s(b_2)\}$ and let $p_1$ and $p_2$ be the two projections from $A$ to $B$, that is, $p_1(b_1, b_2) = b_1$ and $p_2(b_1, b_2) = b_2$. Now prove that $s$ is the coequalizer of $p_1$ and $p_2$.
