The categories of L-convex spaces and L-convergence spaces: extensionality and productivity of quotient maps

Year 2025, Early Access, 1 - 19

Xiancheng Han Bin Pang

https://doi.org/10.15672/hujms.1543634

Abstract

Based on a complete residuated lattice L, we show that the category of L-convex spaces is not extensional and is closed under the formation of finite products of quotient maps. Then we propose the concept of (preconcave, concave) L-convergence spaces via L-co-Scott closed sets and prove that the category of concave L-convergence spaces is isomorphic to that of L-concave spaces. Finally, we investigate the categorical properties of L-convergence spaces and show that it is extensional and closed under the formation of finite products of quotient maps.

Keywords

L-convex space, L-concave space, L-convergence space, Extensionality, Quotient map

Project Number

the Natural Science Foundation of China (Nos. 12471428, 12071033, 12271036)

References

• [1] J. Adámek, H. Herrlich and G.E. Strecker, Abstract and Concrete Categories, Wiley, New York, 1990