Classical homological algebra studies chain complexes, resolutions, and derived functors in additive categories. In this paper we define higher order chain complexes, resolutions, and derived functors in the context of a new type of algebraic structure, called an algebra of left cubical balls. We show that higher order resolutions exist in these algebras, and that they determine higher order Ext-groups. In particular, the Em-term of the Adams spectral sequence (m>2) is such a higher Ext-group, providing a new way of constructing its differentials.
Bibliographical notePublisher Copyright:
© 2014 Elsevier B.V.
ASJC Scopus subject areas
- Algebra and Number Theory