A topological category is a category that is enriched over the category of compactly generated Hausdorff spaces.

8 июн. 2024 г. · A topological category is a concrete category with nice features matching the ability to form weak and strong topologies in Top. 3. Definition.

15 янв. 2012 г. · As Tony pointed out, a topological category in the proposed sense is just a category internal to topological spaces. The notion of internal ... Topological categories as enriched category - MathOverflow Category of topological spaces with open or closed maps What is the right notion of a functor from an internal topological ... The (∞,1)-category of all topological spaces, including the bad ... Другие результаты с сайта mathoverflow.net

In mathematics, the category of topological spaces, often denoted Top, is the category whose objects are topological spaces and whose morphisms are ... As a concrete category · Relationships to other categories

This is a survey for the working mathematician of the theory of initially complete categories. These are concrete categories.

16 дек. 2021 г. · A full concrete subcategory T ′ of T is itself topological over C if and only if it is concretely (co)reflective in T ...

In the category of groups (and homomorphisms) for instance there do not exist arbitrary initial structures, e.g. not every subset of a group is a subgroup.

13 февр. 2024 г. · Just so you know, the name topological category is often used to refer to a category that is enriched over the category of topological spaces.

5 янв. 2023 г. · This course will be an introduction to the interplay between category theory and topology, which permeates much of modern mathematics.

Such categories provide a setting for general topology and topological algebra when X is the category of sets or a category of algebras. It is characteristic ...