An equalizer of $A$ along two morphisms $f, g : A \to B$ can be thought of as a dependent sum over an identity type (see nLab):
$$A|_{f = g} = \sum_{a : A} (f(a) = g(a))$$
Does this idea have a dual? Can we somehow express a coequalizer (quotient type) using dependent products and whatever the "dual of an identity type" is?