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...

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

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

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...

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...

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...

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)...

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

Exosome complex, a multi-protein intracellular complex Protein complex, a group of two or more associated polypeptide chains Species complex, a cluster...

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...

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...

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...

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...

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

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...

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 , … ,...

sets of proteins are called the electron transport chain. In mitochondria, five main protein complexes are involved, whereas prokaryotes have various other...

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...

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...

Ribosome-nascent chain complex (RNC) refers to the collection of molecules that constitute a ribosome attached to the polypeptide (protein) that it is...

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

in an abelian category A {\displaystyle {\mathcal {A}}} but instead chain complexes of objects, so objects in Ch ( A ) {\displaystyle {\text{Ch}}({\mathcal...

differential graded algebra is a graded associative algebra with a chain complex structure that is compatible with the algebra structure. In geometry...

objects of D(A) should be chain complexes in A, with two such chain complexes considered isomorphic when there is a chain map that induces an isomorphism...

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...

homology of the function on the infinite-dimensional manifold. A Floer chain complex is formed from the abelian group spanned by the critical points of the...