Jun 12, 2025 · The nLab records and explores a wide range of mathematics, physics, and philosophy. Where mathematics, physics, and philosophy arise in other fields, computer science and linguistics …

Apr 25, 2025 · Mathematics is the part of science that constructs and studies mathematical objects used to implement mathematical models. The results of study are organized into definitions, theorems, …

Oct 19, 2025 · Later this will lead naturally on to an infinite sequence of steps: first 2-category theory which focuses on relation between relations, morphisms between morphisms: 2-morphism s, then 3 …

Apr 13, 2025 · An overview of algebra concepts, theories, and structures discussed in the nLab mathematical framework.

Nov 13, 2025 · Idea 0.1 The Yoneda lemma says that the set of morphisms from a representable presheaf y (c) into an arbitrary presheaf X is in natural bijection with the set X (c) assigned by X to …

Oct 5, 2025 · On the nLab, we often use the word “2-category” in the general sense of referring to whatever model one may prefer, but usually one in which composition is weak; a bicategory is an …

Jul 28, 2024 · Idea 0.1 In category theory a limit of a diagram F: D → C in a category C is an object lim F of C equipped with morphisms to the objects F (d) for all d ∈ D, such that everything in sight …

Oct 14, 2025 · Idea 0.1 The term ∞ -category broadly refers to higher categories with no bound on the dimension n of their n -morphisms. There are two different ways this is ...

Jun 11, 2025 · A topos is a mathematical structure that generalizes the notion of a topological space and has deep connections with logic and category theory.

Nov 4, 2025 · String diagrams 0.17 Just like monoidal categories, monoidal functors have a string diagram calculus; see these slides for some examples. Related concepts 0.18 monoidal functor, …