Handbook of Categorical Algebra 1

Borceux, F. (1994). Handbook of Categorical Algebra 1: Basic Category Theory. Cambridge University Press.

Type

Book

Intellectual base

Review or monograph

Year

1994

DOI

10.1017/cbo9780511525858

ISBN

9780521441780

DOI registrant

Cambridge University Press

Link

https://doi.org/10.1017/cbo9780511525858

Cited by

4 citations across 4 artifacts.

Domain-specific

• Diagram (category theory)
  • … transfers from A pair of parallel arrows f,g:A⇉B is a diagram whose equalizer is the universal object mapping to A on which f and g agree. to A commutative square diagram expresses compatibility among four objects and four maps; asking whether it is a pullback adds a universal property beyond mere commutativity..
• Kernel (category theory)
  • … composite, universal factorization and uniqueness, monomorphism consequence, existence, equalizer formulation, concrete algebraic realization and distinction from kernel pair are explicit. to An applied instance preserves the same invariant under a changed scale, notation, jurisdiction, dataset, or implementation..
• Nodal decomposition
  • Existence is an extra property of the ambient category; when present the factorization is unique only up to compatible isomorphisms and should not be conflated with ordinary epi-mono image factorization.
• Quotient category
  • Large, enriched, higher-categorical, and object-identifying quotients require size and coherence data beyond this identity.

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