For A a category with finite colimits, we show that the embedding of A into the category of arrows Arr(A) determined by the initial object is the completion of A under strong homotopy cokernels. The nullhomotopy structure of Arr(A) (needed in order to express the notion of homotopy cokernel) is the usual one induced by the canonical string of adjunctions between A and Arr(A).
Keywords: nullhomotopy, homotopy cokernel, arrow category, completion
2020 MSC: 18A30, 18A35, 18N99
Theory and Applications of Categories, Vol. 41, 2024, No. 6, pp 168-193.
Published 2024-03-08.
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