Modulative Categories and Fixed Point Theorems on Modulative Metric Spaces

Year 2025, Early Access, 1 - 21

Utku Gürdal , Elif Uyanık Ekici , Selim Çetin

https://doi.org/10.15672/hujms.1643663

Abstract

In terms of enriched category theory, we obtain a categorical explanation of the concept of modular metric spaces, similar to the case of Lawvere metric spaces. To this end, we introduce a generalization of categories that we call modulative categories, and as an extension of this, we define a new concept of modulative metric spaces along with several other notions. We obtain some results on modulative metric spaces and modulative categories, and illustrate them with examples. Finally, we develop a theory of convergence in modulative metric spaces and generalize some fixed-point theorems to demonstrate the applicability of the results obtained.

Keywords

Enriched category , Fixed point , Lawvere quantale , Modulative metric space

References

• [1] J. Adámek, H. Herrlich and G. Strecker, Abstract and concrete categories, Dover Publications, Mineola, New York, 2009.