Let be a pair of parallel 1-morphisms in a 2-category and let be a pair of parallel 2-morphisms. The equifier of is a universal object equipped with a morphism such that .
More precisely, universality means that for any object , the induced functor
Hom(X,V) \to Hom(X,A)
is fully faithful, and its replete image consists precisely of those morphisms such that . If the above functor is additionally an isomorphism of categories onto the exact subcategory of such , then we say that is a strict equifier.
Equifiers and strict equifiers can be described as a certain sort of weighted 2-limit, where the diagram shape is the walking parallel pair of 2-morphisms , and the weight is the diagram