CatDat

cogenerator

An object QQ of a category is called a cogenerator if for every pair of parallel morphisms f,g:ABf,g : A \to B, f=gf = g holds if for every morphism h:BQh : B \to Q we have hf=hgh \circ f = h \circ g. Equivalently, the functor Hom(,Q):CopSet+\mathrm{Hom}(-,Q) : \mathcal{C}^{\mathrm{op}} \to \mathbf{Set}^+ is faithful. This property refers to the existence of a cogenerator.

Relevant implications

Examples

Counterexamples

Unknown

For these categories the database has no info if they satisfy this property or not.