I have to show that a category $\mathcal{C}$ is coclosed if and only if it has an initial object, a coproduct for every set of objects, and a coequalizer for every pair of morphisms sharing the same domain and codomain.
Now, here's my dilemna. I have no idea what coclosed means, and I've been unable to find any source which gives me an exact definition. And even apart from that, I have no idea how to approach this question. Any help is appreciated, even if it's as limited as providing me with definitions of the terms mentioned in the question.