Handbook of Categorical Algebra, Volume 2¶

Francis Borceux, H. (1994). Handbook of Categorical Algebra, Volume 2: Basic Category Theory. Cambridge University Press.

Type: Book chapter
Intellectual base: Review or monograph
Year: 1994
DOI: 10.1017/cbo9780511525865.010
ISBN: 9780521441797
Link: https://doi.org/10.1017/CBO9780511525865.010

Cited by¶

6 citations across 6 artifacts.

Domain-specific¶

Cosmos (category theory)
- … and symmetry, internal hom and tensor-hom adjunction, completeness and cocompleteness scope, enrichment convention, and any local presentability or model structure assumed are explicit. to An applied instance preserves the same invariant under a changed scale, notation, jurisdiction, dataset, or implementation..
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..
Fibred Category
- … expresses the complementary view: pseudofunctors from the opposite of B to categories correspond, up to the appropriate 2-categorical equivalence, to fibred categories over B. This is why the abstraction is a rigorous home for families and pullback operations that are natural but not strictly equal on the nose.
Groupoid object
- A groupoid object internalizes the data and axioms of a small groupoid in an arbitrary category.
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..
Quotient category
- Large, enriched, higher-categorical, and object-identifying quotients require size and coherence data beyond this identity.

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