An atomic unifunctor is uniquely determined by the category up to equivalence. A category is called atomic if the class of atomic objects is unidense . A category is atomic iff it has an atomic functor. In an atomic category a map is unipotent iff its image under the atomic functor is surjective. X is called unipotent if any non-initial map to X is not disjoint with f .
Unipotent maps are closed under composition and stable under pullbacks.
V such that vs is disjoint with u . Normal monos are closed under composition and stable under pullbacks. A normal coflat mono is called a fraction. Assume the category has pullbacks. Finite limits and finite sums exist.