General Theory of Natural Equivalences

Eilenberg, S., & MacLane, S. (1945). General Theory of Natural Equivalences. Transactions of the American Mathematical Society, 58(2), 231-294.

Type

Journal article

Intellectual base

Primary research

Year

1945

DOI

10.2307/1990284

Link

https://doi.org/10.1090/S0002-9947-1945-0013131-6

Cited from

mathematics

Cited by

4 citations across 4 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Associativity
  • ); category theory (morphism composition is associative by axiom, foundational in Eilenberg-MacLane (1945) theory of natural equivalences

    This sourceThe founding paper of category theory (categories, functors, natural transformations), in which associativity of morphism composition is a defining axiom

• Commutativity
  • In category theory, a commutative diagram expresses that multiple paths from one object to another compose to the same morphism — a generalized form of the commutativity axiom, an idea originating in Eilenberg and Mac Lane (1945) where commuting diagrams are introduced as the natural-equivalence apparatus

    This sourceFounding paper of category theory (category, functor, natural transformation); commuting diagrams appear as the natural-equivalence apparatus — supports the claim that commutative diagrams originate here.

• Isomorphism
  • … Theory of Natural Equivalences", provides the unified language for isomorphism across categories — every category has its own notion of morphism, of isomorphism, and of isomorphism class, and the categorical formulation makes the isomorphism construct a structural primitive across the entire mathematical landscape.

    This source(Foundational paper of category theory, introducing the categories-functors-natural-transformations framework precisely to formalise natural isomorphism as a primary object of study; the categorical formulation generalises the isomorphism construct to any context with a notion of structure and structure-preserving maps, and establishes the natural-versus-unnatural distinction as a structural primitive.)

Domain-specific

• Category theory
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.

Verification

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Links previously used in the corpus

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