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Crossed module information


In mathematics, and especially in homotopy theory, a crossed module consists of groups and , where acts on by automorphisms (which we will write on the left, , and a homomorphism of groups

that is equivariant with respect to the conjugation action of on itself:

and also satisfies the so-called Peiffer identity:

and 21 Related for: Crossed module information

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Crossed module

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In mathematics, and especially in homotopy theory, a crossed module consists of groups G {\displaystyle G} and H {\displaystyle H} , where G {\displaystyle...

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Free module

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free module is a module that has a basis, that is, a generating set consisting of linearly independent elements. Every vector space is a free module, but...

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International Space Station

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connects the large solar panels and radiators to the pressurized modules. The pressurized modules are specialized for research, habitation, storage, spacecraft...

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Homotopy group

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n\geq 3(E)} but for n = 2 {\displaystyle n=2} form the top group of a crossed module with bottom group π 1 ( A ) . {\displaystyle \pi _{1}(A).} There is...

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Double groupoid

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\mathbb {Z} _{4})\cong \mathbb {Z} /2} . Because this is not a trivial crossed-module, it's postnikov invariant is 1 {\displaystyle 1} , giving a homotopy...

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Algebraic topology

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method of simplicial approximation. It contains a lot of material on crossed modules. Fraleigh, John B. (1976), A First Course In Abstract Algebra (2nd ed...

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Module file

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Module file (MOD music, tracker music) is a family of music file formats originating from the MOD file format on Amiga systems used in the late 1980s....

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SIMM

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A SIMM (single in-line memory module) is a type of memory module used in computers from the early 1980s to the early 2000s. It is a printed circuit board...

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Power module

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A power module or power electronic module provides the physical containment for several power components, usually power semiconductor devices. These power...

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Ignition SCADA

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runtime clients. Independent modules provide separate functionality in any or all of the platform components. Ignition SCADA modules provide features such as:...

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Pygame

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Pygame is a cross-platform set of Python modules designed for writing video games. It includes computer graphics and sound libraries designed to be used...

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Gear

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described in the equations above) is not zero, the shafts are crossed. For shafts crossed at right angles, the helix angles are of the same hand because...

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List of gear nomenclature

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on standard practice. A crossed helical gear is a gear that operate on non-intersecting, non-parallel axes. The term crossed helical gears has superseded...

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Thermoelectric cooling

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effect). A thermoelectric module is made from three components; the conductors, legs, and the substrate, and many of these modules are connected electrically...

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Lattice

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whose quotient carries an invariant finite Borel measure Lattice (module), a module over a ring that is embedded in a vector space over a field Lattice...

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Flag of Brazil

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a module (0.33 m) tall. The width of these letters is three-tenths of a module (0.30 m). The conjunction E has a height of three-tenths of a module (0...

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Gene Cernan

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11th human being to walk on the Moon. As he re-entered the Apollo Lunar Module after Harrison Schmitt on their third and final lunar excursion, he remains...

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Vbcc

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to optimize across functions and modules. Target-independent optimizations supported by vbcc include: cross-module function inlining partial inlining...

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Algebra over a field

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zero algebra over a free R-module allows extending this theory as a Gröbner basis theory for submodules of a free module. This extension allows, for...

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Hurewicz theorem

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homotopical excision theorem, involving induced modules for n > 2 {\displaystyle n>2} (crossed modules if n = 2 {\displaystyle n=2} ), which itself is...

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Group cohomology

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actions of a group G in an associated G-module M to elucidate the properties of the group. By treating the G-module as a kind of topological space with elements...

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