Category Theory

Awodey, S. (2010). Category Theory. Oxford University Press.

Type

Book

Intellectual base

Review or monograph

Year

2010

Link

https://global.oup.com/academic/product/category-theory-9780199237180

Cited from

mathematics

Cited by

9 citations across 9 artifacts.

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

Primes

• Disjoint union
  • This conserved decision sequence is the basis for Prime status.
• Equivalence Relation
  • An equivalence relation is not the same as functional dependence in general, although Awodey (2010) establishes the kernel-pair correspondence as the categorical witness that every equivalence relation arises as the kernel of its own quotient map.

    This sourceDevelops the kernel-pair correspondence: every equivalence relation arises as the kernel pair of its own quotient map, formalizing the function-kernel framing.

Domain-specific

• Category of sets
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Classification theorem
  • … relation, invariant or normal form, parameter range and realizability, existence and completeness, uniqueness convention and whether enumeration or equivalence is effective are explicit. to An applied instance preserves the same invariant under changed scale, notation, jurisdiction, dataset, or implementation..
• Dual (category theory)
  • … identity and a convenient observable transfers from A canonical example satisfies the full defining rule of Dual (category theory) with all parameters and conventions explicit. to A careful use of Dual (category theory) tests the constitutive rule and nearest confusable rather than relying on topical resemblance..
• Free category
  • Vertices become objects, edges generate arrows, empty paths are identities and distinct paths remain distinct unless their edge sequences coincide; imposing relations gives a presented category instead.
• Isomorphism of categories
  • … a convenient observable transfers from Renaming every object and morphism bijectively while preserving sources, targets and composition produces an isomorphic category. to A category theorist checks whether inverses hold strictly; if only unit and counit natural isomorphisms exist, the result is equivalence instead..
• Kernel (category theory)
  • Kernels generalize null spaces and normal subobjects, are unique up to unique isomorphism and are dual to cokernels; kernel pairs in categories without zero morphisms are a different construction.
• Opposite category
  • … category, object identity, morphism reversal mapping, identity arrows, reversed composition rule, associativity verification, double-opposite relation and translated dual notions are explicit. to An applied instance preserves the invariant under changed notation, scale, dataset, jurisdiction, or implementation..

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