  We construct what we call a Kirby category, a monoidal category whose
morphisms are smooth 4-manifolds, projecting down to another monoidal category
whose morphisms are orientable 3-manifolds, the projection being induced by the
boundary map on manifolds. We construct a higher categorical generalization of
such concepts and introduce the notion of ribbon $\infty$-categories, a
generalization of braided monoidal $\infty$-categories (\cite{Lu1}), which
gives rise to the concepts of $\infty$-links, $\infty$-4-manifolds as well as
the more general notion of walled $\infty$-4-manifolds if one focuses attention
on $\infty$-4-manifolds built from gluing thickened sheets on ribbons. These
fall into a larger class of constrained $\infty$-4-manifolds whose classical
4-dimensional counterparts are constrained 4-manifolds on which we consider
physical theories. We regard pairs of constrained 4-manifolds and Lagrangians
densities depicting physical theories defined on such spaces as morphism
objects in an enhanced Kirby category, whose objects are regarded as events. We
define a universal category $\Lambda$ of all events that we relate to the
$\infty$-category of ribbon $\infty$-categories and conclude in part that
Lagrangian field theories can be superseded by using $\infty$-categories.
