On injective objects and existence of injective hulls in Q-TOP/(Y,σ)

Abstract

In this paper, motivated by Cagliari and Mantovani, we have obtained a characterization of injective objects (with respect to the class of embeddings in the category Q-TOP of Q-topological spaces) in the comma category Q-TOP/(Y,σ), when (Y,σ) is a stratified Q-topological space, with the help of their T0-reflection. Further, we have proved that for any Q-topological space (Y,σ), the existence of an injective hull of ((X,τ),f) in the comma category Q-TOP/(Y,σ) is equivalent to the existence of an injective hull of its T0-reflection ((˜ X,˜ τ),˜ f ) in the comma category Q-TOP/(Y˜, σ˜ ) (and in the comma category Q-TOP0/(Y˜,σ˜ ), where Q-TOP0 denotes the category of T0-Q-topological spaces) © Shahid Beheshti University