Chain contracting homotopy and a method for relative projective resolutions




Mapping cone, homotopy equivalence, projective class, contracting homotopy


The purpose of this article is to check the main results of the method that allows the construction of a relative projective resolution of an S-module N given in appendix A of the article [1], and to show an application of this method.
It is achieve to show the usefulness of the method, and to put in relevance that the relative projective resolution obtained with the method is comparable to the bar resolution of an algebra because it is provided with chain contracting homotopy.


Guccione JA, Guccione JJ. Hochschild (co)homology of Hopf crossed products. K-theory. 2002; {25(2)}: 138-169.

Félix Y, Tanré D. Topologie Algébrique. Paris : Dunod; 1989.

Eilenberg S, Moore JC. Foundations of Relative Homological Algebra. Mem. Amer. Math. Soc. 55; 1965.

Hilton PJ, Stammbach U. A course in Homological Algebra. New York Heidelberg Berlin : Springer Verlag; 1971.

Ccolque T FC. Caracterización de Proyectivos Relativos e Inyectivos Relativos. Selecciones Matemáticas. 2020; 7(2):276-288.

Hochschild G. Relative Homological Algebra. Trans. Amer. Math. Soc. 1956; 82:246-269.

Cartan H, Eilenberg S. Homological Algebra. New Jersey : Princeton University Press; 1956.



How to Cite

Ccolque Taipe, F. C. (2022). Chain contracting homotopy and a method for relative projective resolutions. Selecciones Matemáticas, 9(01), 102 - 120.