18 нояб. 2023 г. · A category is a quiver (a directed graph with multiple edges) with a rule saying how to compose two edges that fit together to get a new edge. nLab category of monoids · nLab 0-category · nLab (0,1)-category · 2-Category

21 июл. 2024 г. · Category theory is a holistic (structural) approach to mathematics that can (through such methods as Lawvere's ETCS) provide foundations of ... nLab (0,1)-category theory · nLab (∞,2)-category theory · Enriched category

24 сент. 2024 г. · It is the category whose objects are pairs ( c , x ) (c,x) where c c is an object in 𝒞 \mathcal{C} and x x is an element in F ( c ) F(c) and ...

17 сент. 2022 г. · Recall that Cat is generally used to denote the (or a) category (or 2-category) of categories (and functors and natural transformations).

8 авг. 2024 г. · The notion of a 2-category generalizes that of category: a 2-category is a higher category, where on top of the objects and morphisms, there are ... 2-Category theory · Strict 2-categorical · Proarrow equipments · Regular

The nLab is a wiki for research-level notes, expositions and collaborative work, including original research, in mathematics, physics, and philosophy, ...

17 нояб. 2023 г. · A regular category is a finitely complete category which admits a good notion of image factorization. A primary raison d'être behind regular ...

28 февр. 2024 г. · A displayed category over a category C C is the “classifying map” of a category over C C . That is, it is equivalent to the data of a category D ...

4 сент. 2010 г. · Category theory has its place, and that place is significantly lower than some sort of crowning jewel of three fields.

3 июн. 2023 г. · 2. In homotopy type theory. We discuss cartesian products for categories in homotopy type theory. Note: UFP 2013 calls a category a “precategory ...