Is there a comma category functor?
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Yes, there is a comma category functor discussed in the contexts provided. The concept of comma categories is extensively explored in various contexts such as embedding topological spaces into categories, extending Janelidze-Galois theory to two dimensions, and considering categories under specific functors like the free group functor. These discussions involve showing that certain categories can be embedded into comma categories, demonstrating properties of lax comma 2-categories, and exploring the relationships between different types of adjunctions induced by morphisms in 2-categories. The existence and utility of comma categories are highlighted in these research papers, showcasing their significance in various mathematical frameworks .
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| Papers (5) | Insight |
|---|---|
5 Citations | Yes, the paper discusses the existence of a comma category functor in the context of forming codensity triples on a complete category with a specific functor. |
10 Citations | Yes, the paper discusses comma categories in representation theory, indicating the presence of a comma category functor in the context of the research. |
Open access•Posted Content | Yes, the paper discusses how each morphism of a 2-category induces a 2-adjunction between lax comma 2-categories and comma 2-categories, serving as a "change of base functor." |
Open access•Posted Content | Yes, the paper discusses the comma category $(\mathcal{F}\downarrow\mathbf{Grp})$ where groups are under the free group functor, showcasing a technique for embedding categories into comma categories. |
| Yes, the paper discusses comma categories, which are constructed using functors. The comma category functor is utilized in the context of defining and studying comma categories. |
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