%0 Journal Article
%T On injective objects and existence of injective hulls in 𝑄-TOP/(𝑌, 𝜎)
%J Categories and General Algebraic Structures with Applications
%I Shahid Beheshti University
%Z 2345-5853
%A Tiwari, Harshita
%A Srivastava, Rekha
%D 2022
%\ 07/01/2022
%V 17
%N 1
%P 173-202
%! On injective objects and existence of injective hulls in 𝑄-TOP/(𝑌, 𝜎)
%K Injective objects
%K Injective hull
%K T0-reflection
%R 10.52547/cgasa.2022.102640
%X 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).
%U https://cgasa.sbu.ac.ir/article_102640_5e972639559d03b0396400e61c365bb7.pdf