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

5 citations across 5 artifacts.

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

Primes

• 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

• 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.
• 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..

Verification

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