  In this work we introduce partial and global actions of inverse categories on
posets in two variants, fibred actions and actions by symmetries. We study in
detail actions of an inverse category $\mathcal{C}$ on specific subposets of
the poset of finite subsets of $\mathcal{C}$, the Bernoulli actions. We show
that to each fibred action of an inverse category on a poset there corresponds
another inverse category, the semidirect product associated to the action. The
Bernoulli actions give rise to the Szendrei expansions of $\mathcal{C}$, which
define a endofunctor of the category of inverse categories. We extend the
concept of enlargement from inverse semigroup theory to, and we show that if
$\mathcal{D}$ is an enlargement of $\mathcal{C}$ then their Cauchy completions
are equivalent categories; in particular, some pairs corresponding to partial
and global Bernoulli actions are enlargements. We conclude by studying
convolution algebras of finite inverse categories and showing that if
$\mathcal{D}$ is an enlargement of $\mathcal{C}$ then their convolution
algebras are Morita equivalent. Furthermore, using Kan extensions we also
analyze the infinite case.
