Geodesic
On a~strange homotopy category
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 31, Tome 455 (2017), pp. 33-41

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For an additive category $\mathcal C$ in which each morphism has a kernel, it is proved that the homotopy category of the category of complexes over $\mathcal C$ which are concentrated in degrees 2,1,0 and are exact in degrees 2 and 1 is abelian. Under assumption that a category $\mathcal C$ is abelian, earlier this result was obtained by considering the heart of a suitable $t$-structure on the homotopy category of $\mathcal C$. 
@article{ZNSL_2017_455_a3,
     author = {A. I. Generalov},
     title = {On a~strange homotopy category},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {33--41},
     publisher = {mathdoc},
     volume = {455},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a3/}
}
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A. I. Generalov. On a~strange homotopy category. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 31, Tome 455 (2017), pp. 33-41. http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a3/