A note on exactness and stability in homotopical algebra (Q2759193)

The author has developed in [Appl. Categ. Struct. 2, No. 4, 351-406 (1994; Zbl 0826.55015)] an axiomatic for homotopical algebra based on homotopy kernels and cokernels. Following his approach, the author introduces the notions of \(h\)-exactness of an \(h\)-differential sequence (i.e., a nullhomotopy \(0\simeq gf\) of the composition of two consecutive maps of chain complexes). In this context, under suitable stability hypotheses, the exactness properties behave in a simple way and the \(h\)-exactness can be measured by the homotopy type of suitable objects, called homotopical homologies. The notions of exactness agree with the one of \textit{S. Kasangian} and \textit{E. M. Vitale} [Theory Appl. Categ. 7, 47-70 (2000; Zbl 0964.18002)] introduced for symmetric categorical groups. This is a well-written paper which is recommended for the reader interested in the subject.