  The purpose of this article is to propose and investigate a partial order
structure weaker than the lattice structure and which have nice properties
regarding closure operators. We extend accordingly closed pattern mining and
formal concept analysis to such structures we further call confluences. The
primary motivation for investigating these structures is that it allows to
reduce a lattice to a part whose elements are connected, as in some graph,
still preserving a useful characterization of closure operators. Our
investigation also considers how reducing one of the lattice involved in a
Galois connection affects the structure of the closure operators ranges. When
extending this way formal concept analysis we will focus on the intensional
space, i.e. in reducing the pattern language, while recent investigations
rather explored the reduction of the extensional space to connected elements.
