A categorical approach to integration

Abstract

We present a general treatment of measures and integrals in certain (monoidal closed) categories. Under appropriate conditions the integral can be definned by a universal property, and the universal measure is at the same time a universal multiplicative measure. In the multiplicative case this assignment is right adjoint to the formation of the Boolean algebra of idempotents. Now coproduct preservation yields an approach to product measures. © Reinhard Boörger, 2010.