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

Tiwari, Harshita; Srivastava, Rekha

doi:10.52547/cgasa.2022.102640

	On injective objects and existence of injective hulls in 𝑄-TOP/(𝑌, 𝜎)
Categories and General Algebraic Structures with Applications
مقاله 8، دوره 17، شماره 1، مهر 2022، صفحه 173-202 اصل مقاله (459.93 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.52547/cgasa.2022.102640
نویسندگان
Harshita Tiwari^* ؛ Rekha Srivastava
Department of Mathematical Sciences, Indian Institute of Technology, Banaras Hindu University, Varanasi-221005, India.
چکیده
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).
کلیدواژه‌ها
Injective objects؛ Injective hull؛ T0-reflection

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