PlanetPhysics/C 1Category2

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A [[../Cod/|category]]  $𝒞_{1}$  with [[../Coproduct/|coproducts]] is called a  $C_{1}$ -category  if for every family of

of [[../InjectiveMap/|monomorphisms]] ${u_{i} : A_{i} \to B_{i}}$ the [[../TrivialGroupoid/|morphism]] $ι : = \oplus_{i} u_{i} : \oplus_{i} A_{i} \to \oplus_{i} B_{i}$ is also a monomorphism (^[1]).

With certain additional conditions (as explained in ref. ^[1]) $𝒞_{1}$ may satisfy the Grothendieck axiom $𝒜 b 5$ , thus becoming a $C_{3}$ -category (Ch. 11 in ^[1]).

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^[1] ^[2]

References

↑ ^1.0 ^1.1 ^1.2 ^1.3 See p.81 in ref. $[266]$ in the [[../BibliographyForCategoryTheoryAndAlgebraicTopologyApplicationsInTheoreticalPhysics/|Bibliography for categories and algebraic topology]]
↑ Ref. $[288]$ in the [[../BibliographyForCategoryTheoryAndAlgebraicTopologyApplicationsInTheoreticalPhysics/|Bibliography for categories and algebraic topology]]

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[BM266-1] 1.0 ^1.1 ^1.2 ^1.3 See p.81 in ref. $[266]$ in the [[../BibliographyForCategoryTheoryAndAlgebraicTopologyApplicationsInTheoreticalPhysics/|Bibliography for categories and algebraic topology]]

[NP288-2] Ref. $[288]$ in the [[../BibliographyForCategoryTheoryAndAlgebraicTopologyApplicationsInTheoreticalPhysics/|Bibliography for categories and algebraic topology]]

[1]

[2]

PlanetPhysics/C 1Category2

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