where the first arrow is an admissible epimorphism and the second arrow is an admissible monomorphism. Note the morphisms in formula_45 are analogous to the definitions of morphisms in the category of motives, where morphisms are given as correspondences formula_49 such thatformula_50is a diagram where the arrow on the left is a covering map (hence surjective) and the arrow on the right is injective. This category can then be turned into a topological space using the classifying space construction formula_51 , which is defined to be the geometric realisation of the "nerve" of formula_45. Then, the i-th "K"-group of the exact category formula_43 is then defined as