  In this article, we interconnect two different aspects of higher category
theory, in one hand the theory of infinity categories and on an other hand the
theory of 2-categories.We construct an explicit functorial path objet in the
model category of topological categories. We discuss some properties and
consequences of such path object. We also explain the construction of a 2-monad
which algebras are (symmetric) monoidal topological categories. Finally, we
explain the relationship with the eventual model structure on the category of
T-algebras.
