Linked from

The 26 pages that link to Category theory, each with the reason it gives.

• SetNarrower topic: It offers a structural viewpoint in which sets and functions form a basic example.

• Set theoryCompared with: It offers a structural language that can complement or challenge set-based foundations.

• Abstract algebraNarrower topic: Its language generalizes the maps and constructions used throughout abstract algebra.

• Universal propertyNarrower topic: Universal properties are commonly expressed as patterns of objects and morphisms in categories.

• Homological algebraNarrower topic: Categorical language lets homological methods apply across modules, groups, and other settings.

• IsomorphismNarrower topic: Its abstract language defines isomorphisms uniformly across different kinds of mathematical objects.

• Alexander GrothendieckRelated: Grothendieck used categorical language to express constructions uniformly across algebraic geometry.

• OntologyCompared with: Its formal use of “objects” can be mistaken for claims about what exists metaphysically.

• Commutative algebraRelated: Categorical language organizes rings, modules, and the functors connecting them.

• Natural transformationNarrower topic: Natural transformations emerged as a basic part of category theory’s formal language.

• Samuel EilenbergBroader topic: Eilenberg and Saunders Mac Lane introduced this framework in 1945.

• MorphismNarrower topic: Morphism is one of the two basic kinds of data in this framework.

• Nicolas BourbakiCompared with: Category theory offers a different language for unification than Bourbaki’s set-theoretic foundations.

• Philosophy of mathematicsRelated: Its structural language offers alternative ways to organize and interpret mathematical foundations.

• Universal algebraCompared with: Category theory emphasizes maps and structural relationships rather than equational presentations of algebras.

• Yoneda lemmaNarrower topic: The lemma is a general theorem about objects and morphisms in categories.

• Axiomatic systemRelated: Categorical foundations organize mathematics through relationships and universal properties instead of membership axioms.

• Mathematical structureRelated: It compares structures through maps that preserve their defining features.

• Saunders Mac LaneNarrower topic: Mac Lane helped establish this framework and its basic language.

• Order theoryRelated: A preorder can be viewed as a category with at most one arrow between objects.

• Snake lemmaNarrower topic: Categorical formulations explain why the lemma applies beyond modules and groups.

• Von Neumann–Bernays–Gödel set theoryRelated: Proper classes allow large categories, such as the category of all sets, to be discussed directly.

• Five lemmaNarrower topic: Categorical language expresses the five lemma for structures beyond groups and modules.

• Adjoint functorsNarrower topic: Adjunctions are defined using categories, functors, and morphisms.

• Nine lemmaNarrower topic: The lemma's formulation in abelian categories reflects its categorical generality.

• Axiom (computer algebra)Narrower topic: Axiom’s categories borrow the idea of specifying shared operations abstractly.