In mathematics, a chain complex is an algebraic structure that consists of a sequence of abelian groups (or modules) and a sequence of homomorphisms between...

An electron transport chain (ETC) is a series of protein complexes and other molecules which transfer electrons from electron donors to electron acceptors...

usages. The most direct usage of the term is to take the homology of a chain complex, resulting in a sequence of abelian groups called homology groups. This...

a k-chain is a formal linear combination of the k-cells in a cell complex. In simplicial complexes (respectively, cubical complexes), k-chains are combinations...

-dimensional boundary – induces the singular chain complex. The singular homology is then the homology of the chain complex. The resulting homology groups are the...

especially topology, a Poincaré complex (named after the mathematician Henri Poincaré) is an abstraction of the singular chain complex of a closed, orientable...

sometimes called the cytochrome bc1 complex, and at other times complex III, is the third complex in the electron transport chain (EC 1.10.2.2), playing a critical...

with the emergence of category theory. A central concept is that of chain complexes, which can be studied through their homology and cohomology. Homological...

chain complexes and the category of simplicial abelian groups. Moreover, under the equivalence, the n {\displaystyle n} th homology group of a chain complex...

hypothesis. An example of graded vector space is associated to a chain complex, or cochain complex C of vector spaces; the latter takes the form 0 → C 0 ⟶ d...

operator and the chain complex are defined similarly to those for simplicial complexes. More general are cell complexes. A chain complex ( C ∗ , ∂ ∗ ) {\displaystyle...

dehydrogenase and mitochondrial complex I) is the first large protein complex of the respiratory chains of many organisms from bacteria to humans. It catalyzes the...

cellular-homology modules are defined as the homology groups Hi of the cellular chain complex ⋯ → C n + 1 ( X n + 1 , X n ) → C n ( X n , X n − 1 ) → C n − 1 ( X...

In mathematics, and specifically in topology, a CW complex (also cellular complex or cell complex) is a topological space that is built by gluing together...

The branched-chain α-ketoacid dehydrogenase complex (BCKDC or BCKDH complex) is a multi-subunit complex of enzymes that is found on the mitochondrial inner...

definition of the cohomology of the dual of a chain complex. Let R be a commutative ring, C a chain complex of R-modules and G an R-module. Just as one...

homomorphism associated to a chain map from the chain complex of S to the chain complex of T. Explicitly, this chain map is given on k-chains by f ( ( v 0 , … ,...

The cohomology of the cohomology again formed a chain complex, and its cohomology formed a chain complex, and so on. The limit of this infinite process...

sequences linked by chain complexes (that is, a short exact sequence of chain complexes, or from another point of view, a chain complex of short exact sequences)...

sets of proteins are called the electron transport chain. In eukaryotes, five main protein complexes are involved, whereas in prokaryotes many different...

homology groups of a simplicial complex, one can read the corresponding chain complex directly, provided that consistent orientations are made of all simplices...

mathematics, the homotopy category K(A) of chain complexes in an additive category A is a framework for working with chain homotopies and homotopy equivalences...

category. Note that in addition to using a 2-term chain complex, would could instead consider a chain complex A ∙ ∈ C h ≤ 0 ( Ab ) {\displaystyle A^{\bullet...

Euler characteristic of any chain complex to be the alternating sum of the ranks of the homology groups of the chain complex, assuming that all these ranks...

generalization of chain complexes, the homology groups of the chain complex becoming the homotopy groups of the “non-commutative chain complex” or stack. -...

a particular long exact sequence in the homology groups of certain chain complexes. The result is valid in every abelian category. In an abelian category...

gluconeogenesis of the Cori cycle, particularly the mitochondrial respiratory chain complex 1. The buildup of lactate and its substrates for lactate production...

Grassmannian. chain homotopy Given chain maps f , g : ( C , d C ) → ( D , d D ) {\displaystyle f,g:(C,d_{C})\to (D,d_{D})} between chain complexes of modules...

are derived intersections of zero loci. First, the Koszul complex Ks of (A,s) is a chain complex: the composition of any two maps is zero. Second, the map...

A supply chain is a complex logistics system that consists of facilities that convert raw materials into finished products and distribute them to end consumers...