Integrals Along Bimonoid Homomorphisms

We introduce a notion of an integral along bimonoid homomorphism as simultaneous generalization the and cointegral bimonoids. The purpose this paper is to characterize existence specific integral, called normalized generator in terms kernel cokernel homomorphism. volume on abelian category dimension vector spaces order groups. In applications, we show that there exists nontrivial partially defined bicommutative Hopf monoids. yields Fredholm homomorphisms between monoids, which gives analogue index theory. This technical preliminary our subsequent about construction TQFT’s.