An AB3 category has colimits Visit http://stacks.math.columbia.edu/tag/079A

There is one sentence I can't prove. Quoted as"If an abelian category has direct sums (i.e., AB3), then it has colimits."


And in this page http://stacks.math.columbia.edu/tag/002P It says that "If all coproducts and coequalizers exist, all colimits exist".

The latter one asks for the existence of coequalizer but the former one does not.I am confused about it.
As far as I know,R-mod category with objects indexed by a set has arbitrary colimit,which is defined as a quotient mod.So when it comes to an abelian category,  based on which could I get the colimit?
I'll appreciate it if anyone gives some hints.
 A: Given two morphisms $f,g\colon A\to B$ in an abelian category $A$, the coequalizer is given by coker$(f-g)$. To show this assume there is an $A$-morphism $h\colon B\to T$ such that $hf=hg$. Then we have $0=hf-hg=h(f-g)$. So by the universal property of cokernels we have the universal property of coequalizers as well. 
A: Assuming an abelian category is defined as a category satisfying:
(1) there is a zero object
(2) binary products and coproducts exist
(3) kernels and cokernels exist
(4) monomorphisms are kernels and epimorphisms are cokernels
Since the axioms of an abelian category are self dual, I will give hints to explain why an abelian category has equalizers.


*

*Suppose that $f:A\to C$ is a monomorphism and $g:B\to C$ is a morphism in an abelian category. It follows by (4) that $f$ is a kernel of some morhism $h:C\to D$. Show that if $q :P \to B$ is the kernel of $hg$, then there is a morphism $p:P\to A$ such that $(P,p,q)$ is the pullback of $f$ and $g$.

*Show that in a category with binary products and pullbacks of monomorphisms, equalizers exists. (Hint: for a pair of morphisms $f,g :A \to B$ consider the morphisms $\langle 1,f\rangle,\langle 1,g\rangle : A \to A\times B$).

*Use 1 and 2 to prove that an abelian category has equalizers.
