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Everything about Chain complex
Tool in homological algebra
In mathematics, a chain complex is an algebraic structure that consists of a sequence of abelian groups and a sequence of homomorphisms between consecutive groups such that the image of each homomorphism is contained in the kernel of the next. Associated to a chain complex is its homology, which is a measure of the failure of a chain complex to be exact. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Chain complexA 5-minute orientation
- Skim a recent paper: Complex regulatory effects of gut microbial short-chain fatty acids on immune tolerance and autoimmunityInfluential work since 2022
- Pick up a classic book: Robust Manufacturing ControlThe most-reprinted book on the subject
- Read the landmark paper: Profiling of complex microbial populations by denaturing gradient gel electrophoresis analysis of polymerase chain reaction-amplified genes coding for 16S rRNACited 9,176 times
- Go sideways: Differential graded algebraA closely related topic
- Go sideways: André–Quillen cohomologyA closely related topic
📖 Definitions
Noun A sequence of Abelian groups (or modules), together with a sequence of homomorphisms (called boundary homomorphisms) between consecutive groups, such that the image of one homomorphism is contained in the kernel of the next.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Profiling of complex microbial populations by denaturing gradient gel electrophoresis analysis of polymerase chain reaction-amplified genes coding for 16S rRNA
Supply-chain networks: a complex adaptive systems perspective
A complex network approach to supply chain network theory
The respiratory‐chain NADH dehydrogenase (complex I) of mitochondria
Respiratory chain complex I deficiency
Building a complex complex: Assembly of mitochondrial respiratory chain complex I
Optimizing Chain Bridging in Complex Block Copolymers
Structural characteristics of complex supply chain networks
🆕 Influential since 2022
Complex regulatory effects of gut microbial short-chain fatty acids on immune tolerance and autoimmunity
Complexities of the global plastics supply chain revealed in a trade-linked material flow analysis
Mesostructural characteristics and evaluation of asphalt mixture contact chain complex networks
Deep learning approaches to identify order status in a complex supply chain
Conceptualizing Supply Chain Resilience: The Role of Complex IT Infrastructures
📚 Books worth reading
Robust Manufacturing ControlKatja Windt · 2012
Mitochondrial Oxidative Phosphorylation Nuclearencoded Genes Enzyme Regulation And PathophysiologyBernhard Kadenbach · 2012
Network Scheduling Techniques for Construction Project ManagementMiklós Hajdu · 1997
Optimization Approaches For Solving String Selection ProblemsPanos M. Pardalos · 2013- 📕Women in topologyMaria Basterra, Kristine Bauer · 2015
- 📕Topics in Hyperplane ArrangementsMarcelo Aguiar, Swapneel Mahajan · 2017
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Differential graded algebra In mathematics – particularly in homological algebra, algebraic topology, and algebraic geometry – a differential graded algebra (or DGA, or DG algebra)…
- André–Quillen cohomology In commutative algebra and algebraic geometry, André–Quillen cohomology is a cohomology theory for commutative rings and their modules, constructed using…
- Homotopy associative algebra In mathematics, an algebra such as ( R , + , ⋅ ) {\displaystyle (\mathbb {R} ,+,\cdot )} has multiplication ⋅ {\displaystyle \cdot } whose associativity…
- Homotopy category of chain complexes In homological algebra in mathematics, the homotopy category K(A) of chain complexes in an additive category A is a framework for working with chain homotopies…
- Eilenberg–Moore spectral sequence In mathematics, in the field of algebraic topology, the Eilenberg–Moore spectral sequence addresses the calculation of the homology groups of a pullback…
- Derived category In mathematics, the derived category D(A) of an abelian category A is a construction of homological algebra introduced to refine and in a certain sense…
- Hochschild homology In mathematics, Hochschild homology (and cohomology) is a homology theory for associative algebras over rings. There is also a theory for Hochschild homology…
- 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…