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2009β€’Georgian Mathematical JournalRequires access

Abelian Categories Versus Abelian 2-Categories

Teimuraz Pirashvili

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Abstract

Recently Dupont proved that the categories of discrete and codiscrete (or connected) objects in an abelian 2-category are equivalent abelian categories. In this paper for any abelian category 𝔸 with enough projective or injective objects we construct an abelian 2-category 𝔗 such that the categories of discrete, resp. codiscrete objects of 𝔗 are equivalent to 𝔸.

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What this paper is about

Recently Dupont proved that the categories of discrete and codiscrete (or connected) objects in an abelian 2-category are equivalent abelian categories. In this paper for any abelian category 𝔸 with enough projective or injective objects we construct an abelian 2-category 𝔗 such that the categories of discrete, resp. codiscrete objects of 𝔗 are equivalent to 𝔸.

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Available abstract

Recently Dupont proved that the categories of discrete and codiscrete (or connected) objects in an abelian 2-category are equivalent abelian categories. In this paper for any abelian category 𝔸 with enough projective or injective objects we construct an abelian 2-category 𝔗 such that the categories of discrete, resp. codiscrete objects of 𝔗 are equivalent to 𝔸.

Key concepts: Abelian group, Abelian category, Mathematics, Rank of an abelian group, Divisible group, Elementary abelian group, Pure mathematics, Torsion subgroup

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