Normed categories as a common forum for monoid entropy and Banach’s Fixed Point Theorem.

‎‎‎Both, normed monoids and metric spaces, are examples of small normed categories. With an appropriate notion of normed sequential convergence we discuss to which extent they provide a common environment for establishing generalizations of Banach’s Fixed Point Theorem and of notions of entropy as developed for many mathematical structures by Dikranjan and Giordano Bruno.