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homological form

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  • Homological algebra — is the branch of mathematics which studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology (a precursor to algebraic topology) and abstract… …   Wikipedia

  • Homological mirror symmetry — is a mathematical conjecture made by Maxim Kontsevich. It seeks a systematic mathematical explanation for a phenomenon called mirror symmetry first observed by physicists studying string theory.In an address to the 1994 International Congress of… …   Wikipedia

  • Mapping cone (homological algebra) — In homological algebra, the mapping cone is a construction on a map of chain complexes inspired by the analogous construction in topology. In the theory of triangulated categories it is a kind of combined kernel and cokernel: if the chain… …   Wikipedia

  • List of important publications in mathematics — One of the oldest surviving fragments of Euclid s Elements, found at Oxyrhynchus and dated to circa AD 100. The diagram accompanies Book II, Proposition 5.[1] This is a list of important publications in mathematics, organized by field. Some… …   Wikipedia

  • List of lemmas — This following is a list of lemmas (or, lemmata , i.e. minor theorems, or sometimes intermediate technical results factored out of proofs). See also list of axioms, list of theorems and list of conjectures. 0 to 9 *0/1 Sorting Lemma ( comparison… …   Wikipedia

  • Triangulated category — A triangulated category is a mathematical category satisfying some axioms that are based on the properties of the homotopy category of spectra, and the derived category of an abelian category. A t category is a triangulated category with a t… …   Wikipedia

  • Injective module — In mathematics, especially in the area of abstract algebra known as module theory, an injective module is a module Q that shares certain desirable properties with the Z module Q of all rational numbers. Specifically, if Q is a submodule of some… …   Wikipedia

  • List of mathematics articles (H) — NOTOC H H cobordism H derivative H index H infinity methods in control theory H relation H space H theorem H tree Haag s theorem Haagerup property Haaland equation Haar measure Haar wavelet Haboush s theorem Hackenbush Hadamard code Hadamard… …   Wikipedia

  • Group cohomology — This article is about homology and cohomology of a group. For homology or cohomology groups of a space or other object, see Homology (mathematics). In abstract algebra, homological algebra, algebraic topology and algebraic number theory, as well… …   Wikipedia

  • Derived category — In mathematics, the derived category D(C) of an abelian category C is a construction of homological algebra introduced to refine and in a certain sense to simplify the theory of derived functors defined on C. The construction proceeds on the… …   Wikipedia

  • Nakayama lemma — In mathematics, more specifically modern algebra and commutative algebra, Nakayama s lemma also known as the Krull–Azumaya theorem[1] governs the interaction between the Jacobson radical of a ring (typically a commutative ring) and its finitely… …   Wikipedia

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