We study the glueing constructions (comma objects) on general algebraic structures on a 2-category, described in terms of 2-monads and adjunctions. Specifically, lifting theorems for the comma objects and change-of-base results on both algebras of 2-monads and adjunctions in a 2-category are presented. As a leading example, we take the 2-monad on Cat whose algebras are symmetric monoidal categories, and show that many of the constructions in our previous work on models of linear type theories can be derived within this axiomatics. 1 Introduction In the previous work [2, 3] we have considered a glueing construction for symmetric monoidal (closed) categories, for studying the logical predicates for models of linear type theories. In that construction the glueing functor is supposed to be lax symmetric monoidal, thus preserves the structure only up to a few coherent morphisms, not up to isomorphisms or identity. From a view of the study of categories with algebraic structures [8] (which...