In this talk we will present recent results on effective descent morphisms of the lax comma category Ord//X, which improve results obtained in [2]. While in [3] effective descent morphisms of Ord, and consequently of the comma category Ord/X, were obtained making use of the category of relations, here we will embed Ord//X in the category of filtered preorders, as defined in [1].

[1] M.M. Clementino, G. Janelidze, Effective descent morphisms of filtered preorders, Preprint 23-37, DMUC (2023).
[2] M.M. Clementino, F. Lucatelli Nunes, On lax comma categories of ordered sets, Quaest. Math. 46 (S1) (2023) 145-159.
[3] G. Janelidze, M. Sobral, Finite preorders and topological descent I, J. Pure Appl. Algebra 175 (1-3) (2002), 187-205.