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".
Keywords: homotopy limit, bilimit, bicategory of fractions, factorization system, arrow category, 2-abelian bicategory
2020 MSC: 18A32, 18E10, 18E35, 18G45, 18N10
Theory and Applications of Categories, Vol. 41, 2024, No. 51, pp 1812-1872.
Published 2024-11-14.
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