Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585317120220701On injective objects and existence of injective hulls in 𝑄-TOP/(𝑌, 𝜎)17320210264010.52547/cgasa.2022.102640ENHarshita TiwariDepartment of Mathematical Sciences, Indian Institute of Technology,
Banaras Hindu University, Varanasi-221005, India.Rekha SrivastavaDepartment of Mathematical Sciences, Indian Institute of Technology,
Banaras Hindu University, Varanasi-221005, India.Journal Article20220813In 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-<strong>TOP</strong> of 𝑄-topological spaces) in the comma category 𝑄-<strong>TOP</strong>/(𝑌,𝜎), when (𝑌,𝜎) is a stratified 𝑄-topological space, with the help of their 𝑇<sub>0</sub>-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-<strong>TOP</strong>/(𝑌, 𝜎) is equivalent to the existence of an injective hull of its 𝑇<sub>0</sub>-reflection ((𝑋 ̃,𝜏 ̃), 𝑓 ̃) in the comma category Q-<strong>TOP</strong>/(𝑌 ̃, 𝜎 ̃ ) (and in the comma category 𝑄-<strong>TOP</strong><sub>0</sub>/(𝑌 ̃, 𝜎 ̃ ), where 𝑄-<strong>TOP</strong><sub>0</sub> denotes the category of 𝑇<sub>0</sub>-𝑄-topological spaces).https://cgasa.sbu.ac.ir/article_102640_5e972639559d03b0396400e61c365bb7.pdf