Meanings
- uncountablealgebraThe branch of mathematics dealing with homology and in particular with homological functors and the algebraic structures they entail.
The notion of chain complex is central to homological algebra.
4 more examples
The development of homological algebra was closely intertwined with the emergence of category theory.
Homological algebra for our purposes consists of studying certain abelian groups Hⁿ(G,A) and H#95;n(G,A), known as the nth cohomology and homology groups of the group G with coefficients in the G-module A.
2002, C. R. Leedham-Green, S. McKay, The Structure of Groups of Prime Power Order, Oxford University Press, page 171A similar shift of interpretation of CT took place at about the same time in another context, namely homological algebra.
2007, Ralph Krömer, Tool and Object: A History and Philosophy of Category Theory, Springer (Birkhäuser), page 93In Section 4.1, we shall introduce some minimal amount of homological algebra needed to launch singular homology.
2014, Anant R. Shastri, Basic Algebraic Topology, Taylor & Francis (CRC Press / Chapman & Hall), page 169
Translations
German homologische Algebra
- homologische Algebrabranch of algebra
Italian algebra omologica
- algebra omologicabranch of algebra
Polish algebra homologiczna
- algebra homologicznabranch of algebra
Cite this entry
homological algebra. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/homological%20algebra
“homological algebra.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/homological%20algebra. Accessed November 5, 2026.
WatkinsX Dictionary, s.v. “homological algebra,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/homological%20algebra.
Source: homological algebra on Wiktionary, CC BY-SA 4.0.