Geodesic
From abelian categories to 2-abelian bicategories
Theory and applications of categories, Tome 41 (2024), pp. 1812-1872

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We show that, if A is an abelian category, then a certain bicategory of fractions Arr(A)[Σ^{-1}] of the 2-category Arr(A) in A is 2-abelian. On the way, we study homotopy kernels and homotopy cokernels, their relationship with 2-limits and bilimits, and how they pass through the general construction of the bicategory of fractions. We also introduce two new factorization systems in A and we use them to describe the class Σ of "weak equivalences".

Publié le :
Classification : 18A32, 18E10, 18E35, 18G45, 18N10
Keywords: homotopy limit, bilimit, bicategory of fractions, factorization system, arrow category, 2-abelian bicategory 
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     author = {Enrico M. Vitale},
     title = {From abelian categories to 2-abelian bicategories},
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     url = {http://geodesic.mathdoc.fr/item/TAC_2024_41_a50/}
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Enrico M. Vitale. From abelian categories to 2-abelian bicategories. Theory and applications of categories, Tome 41 (2024), pp. 1812-1872. http://geodesic.mathdoc.fr/item/TAC_2024_41_a50/