Mathematics > Home > Advances in Pure and Applied Mathematics > Issue 4 (September 2024) > Article
Moncef Ghazel
University of Tunis El manar
Published on 18 September 2024 DOI : 10.21494/ISTE.OP.2024.1199
We use pointwise Kan extensions to generate new subcategories out of old ones. We investigate the properties of these newly produced categories and give sufficient conditions for their cartesian closedness to hold. Our methods are of general use. Here we apply them particularly to the study of the properties of certain categories of fibrewise topological spaces. In particular, we prove that the categories of fibrewise compactly generated spaces, fibrewise sequential spaces and fibrewise Alexandroff spaces are cartesian closed provided that the base space satisfies the right separation axiom.
We use pointwise Kan extensions to generate new subcategories out of old ones. We investigate the properties of these newly produced categories and give sufficient conditions for their cartesian closedness to hold. Our methods are of general use. Here we apply them particularly to the study of the properties of certain categories of fibrewise topological spaces. In particular, we prove that the categories of fibrewise compactly generated spaces, fibrewise sequential spaces and fibrewise Alexandroff spaces are cartesian closed provided that the base space satisfies the right separation axiom.
Reflective subcategory Reflective hull Dense functor Kan extension Codensity monad Cartesian closed category Fibrewise topological space
Reflective subcategory Reflective hull Dense functor Kan extension Codensity monad Cartesian closed category Fibrewise topological space