An Introduction to Homological Algebra

Charles A. Weibel, A. I. t. H. A., & Press, C. U. (1994). An Introduction to Homological Algebra. Cambridge University Press.

Type

Book

Intellectual base

Textbook

Year

1994

DOI

10.1017/cbo9781139644136

ISBN

9780521435000

Link

https://doi.org/10.1017/cbo9781139644136

Cited by

9 citations across 9 artifacts.

Domain-specific

• Cokernel
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Derived functor
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Five lemma
  • The five lemma states, in its standard form, that in a commutative diagram of exact five-term rows, if the second and fourth vertical maps are isomorphisms, the first is an epimorphism, and the fifth is a monomorphism, then the middle vertical map is an isomorphism.
• Five-term exact sequence
  • Under a standard cohomological convention it has the form 0 to E2(1,0) to H1 to E2(0,1) to E2(2,0) to H2, with indexing and edge-map direction changed in homological or other conventions.
• Lie Algebra Extension
  • The extension records not just the two component algebras but how their brackets are coupled.
• Nine lemma
  • … constitutive identity and a convenient observable transfers from A canonical example satisfies the full defining rule of Nine lemma with its carrier, parameters and conventions explicit. to A careful use of Nine lemma tests its assumptions, boundary and nearest confusable rather than relying on the name alone..
• Tower of objects
  • A tower is a functor from the reversed natural-number order, maps need not be inclusions and its inverse limit is an additional construction rather than the tower itself.
• Weak dimension
  • … instance directly demonstrates that the ring side and module category are fixed and the stated supremum of flat dimensions or equivalent Tor-vanishing threshold is used consistently. to An applied instance preserves the same invariant under a changed scale, notation, jurisdiction, dataset, or implementation..
• Zig-zag lemma
  • … chain complexes and short exact sequence, chain maps and degrees, homology groups, lift choices, connecting morphism sign convention, well-definedness, naturality and exactness are explicit. to An applied instance preserves the same invariant under changed scale, notation, dataset, jurisdiction, or implementation..

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