  A recollement is a decomposition of a given category (abelian or
triangulated) into two subcategories with functorial data that enables the
glueing of structural information. This paper is dedicated to investigating the
behaviour under glueing of some basic properties of abelian categories
(well-poweredness, Grothendieck's axioms AB3, AB4 and AB5, existence of a
generator) in the presence of a recollement. In particular, we observe that in
a recollement of a Grothendieck abelian category the other two categories
involved are also Grothendieck abelian and, more significantly, we provide an
example where the converse does not hold and explore multiple sufficient
conditions for it to hold.
