TY - JOUR
ID - 102640
TI - On injective objects and existence of injective hulls in 𝑄-TOP/(𝑌, 𝜎)
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Tiwari, Harshita
AU - Srivastava, Rekha
AD - Department of Mathematical Sciences, Indian Institute of Technology,
Banaras Hindu University, Varanasi-221005, India.
Y1 - 2022
PY - 2022
VL - 17
IS - 1
SP - 173
EP - 202
KW - Injective objects
KW - Injective hull
KW - T0-reflection
DO - 10.52547/cgasa.2022.102640
N2 - 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).
UR - https://cgasa.sbu.ac.ir/article_102640.html
L1 - https://cgasa.sbu.ac.ir/article_102640_5e972639559d03b0396400e61c365bb7.pdf
ER -