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

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 𝑄TOP of 𝑄topological spaces) in the comma category 𝑄TOP/(𝑌,𝜎), when (𝑌,𝜎) is a stratified 𝑄topological space, with the help of their 𝑇0reflection. Further, we have proved that for any 𝑄topological space (𝑌,𝜎), the existence of an injective hull of ((𝑋, 𝜏), 𝑓 ) in the comma category 𝑄TOP/(𝑌, 𝜎) is equivalent to the existence of an injective hull of its 𝑇0reflection ((𝑋 ̃,𝜏 ̃), 𝑓 ̃) in the comma category QTOP/(𝑌 ̃, 𝜎 ̃ ) (and in the comma category 𝑄TOP0/(𝑌 ̃, 𝜎 ̃ ), where 𝑄TOP0 denotes the category of 𝑇0𝑄topological spaces).