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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
Crossed_module
In mathematics, a module that has a basis
mathematics, a free module is a module that has a basis, that is, a generating set that is linearly independent. Every vector space is a free module, but, if the
Free_module
British mathematician (1904–1960)
conjecture led to the creation of the Whitehead manifold. The definition of crossed modules is due to him. He also made important contributions in differential
J._H._C._Whitehead
\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
Double_groupoid
properties of 2-groups are already known. 2-groups can be described using crossed modules and their classifying spaces. Essentially, these are given by a quadruple
N-group_(category_theory)
Study of categorified structures
theory Grothendieck topology Topological dynamics Categorical dynamics Crossed module Pseudoalgebra 2-ring Lie n-algebra "Double Categories and Pseudo Algebras"
Higher-dimensional_algebra
Enterprise resource planning by SAP SE
management, and simplified landscape deployment. The update also improved cross-module traceability, allowing audit and change tracking across distributed systems
SAP_S/4HANA
Mathematical theorem
the category of groupoids turns out to be equivalent to the notion of crossed module. This leads to the idea of using multiple groupoid objects in homotopy
Eckmann–Hilton_argument
Bialgebra Bicategory Convolution product Crossed module Double groupoid Higher-dimensional algebra Hopf algebra Module (mathematics) Ring (mathematics) Mosa
R-algebroid
Algebraic construct classifying topological spaces
n\geq 3} 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
Homotopy_group
Organizing code into modules
into independent modules, each providing an aspect of a computer program in its entirety without providing other aspects. A module interface expresses
Modular_programming
Modular space station in low Earth orbit
plans for the ISS include the addition of at least one module, the Payload Power Thermal Module by Axiom Space, forming the commercial segment of the station
International_Space_Station
Scheme-based programming language implementation
scrutinizer does not allow cross-module flow analysis, so it can only be used to optimize code that's part of one compiling unit (or module). CHICKEN Scheme was
Chicken (Scheme implementation)
Chicken_(Scheme_implementation)
Python module for writing video games
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
Pygame
Branch of mathematics
theory Pursuing Stacks Shape theory Moduli stack of formal group laws Crossed module Milnor's theorem on Kan complexes Fibration of simplicial sets Shape
Homotopy_theory
Motor vehicle platform
The Common Module Family (CMF) is a modular architecture concept jointly developed by car manufacturers Nissan and Renault through their Renault–Nissan–Mitsubishi
Renault–Nissan Common Module Family
Renault–Nissan_Common_Module_Family
Vacuum tube used in transmitters
A crossed-field amplifier (CFA) is a specialized vacuum tube, first introduced in the mid-1950s and frequently used as a microwave amplifier in very-high-power
Crossed-field_amplifier
Electronics module
A power module or power electronic module provides the physical containment for several power components, usually power semiconductor devices. These power
Power_module
Hypothesis in mathematical category theory
is still open.[citation needed] See also: Eilenberg–MacLane space, crossed module. Algebraic homotopy N-group (category theory) Pursuing Stacks Quasi-category
Homotopy_hypothesis
System-on-a-chip microcontroller model with Wi-Fi
community in August 2014 via the ESP-01 module, made by a third-party manufacturer Ai-Thinker. This small module allows microcontrollers to connect to a
ESP8266
Multinational wheeled armoured fighting vehicle
drive module and interchangeable mission modules which allow several configurations to meet different operational requirements. The drive module has been
Boxer (armoured fighting vehicle)
Boxer_(armoured_fighting_vehicle)
Family of file formats
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.
Module_file
Gives a homomorphism from homotopy groups to homology groups
homotopical excision theorem, involving induced modules for n > 2 {\displaystyle n>2} (crossed modules if n = 2 {\displaystyle n=2} ), which itself is
Hurewicz_theorem
Vector space equipped with a bilinear product
with "commutative ring" and "module". Unital zero algebras allow the unification of the theory of submodules of a given module and the theory of ideals of
Algebra_over_a_field
to optimize across functions and modules. Target-independent optimizations supported by vbcc include: cross-module function inlining partial inlining
Vbcc
Branch of mathematics
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
Algebraic_topology
methods". Cubical omega-groupoids, higher homotopy groupoids, crossed modules, crossed complexes and Galois groupoids are key concepts in developing applications
Nonabelian_algebraic_topology
Tools for studying groups based on techniques from algebraic topology
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
Group_cohomology
Switch between light-conducting fiber circuits
demultiplexers. The electronic signals are then switched by an electronic switch module. Finally, the switched electronic signals are converted back into optical
Optical_cross-connect
Polyhedron whose vertices represent permutations
Graduate Texts in Mathematics 152. Huebschmann, J. (2012), "Braids and crossed modules", Journal of Group Theory, 15: 57–83, arXiv:0904.3895, doi:10.1515/JGT
Permutohedron
of crossed groups over a site". arXiv:1702.02128 [math.AG]. - gives techniques for defining sheaf cohomology with coefficients in a crossed module, or
Abelian_2-group
addresses of externally referenced objects and functions, various kinds of cross module checks (e.g. type checks on externally visible identifiers and in some
Link_time
American dark electronic band
Module is an American dark electronic band founded in 1999 from Orlando, Florida. Since 2006 they have been based out of Washington state. God Module
God_Module
Rotating circular machine part with teeth that mesh with another toothed part
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
Gear
Primary US ISS module
The Destiny module, also known as the U.S. Lab, is the primary operating facility for U.S. research payloads aboard the International Space Station (ISS)
Destiny_(ISS_module)
Computer memory module
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
SIMM
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
Flag_of_Brazil
Microwave Power Module Panel, supported by the US Naval Research Laboratory. While the eventual goal was to design a power module with a cross section as small
Microwave_power_module
Infinite-dimensional group in topology
Elliptic cohomology String bordism Jurco, Branislav (August 2011). "Crossed Module Bundle Gerbes; Classification, String Group and Differential Geometry"
String_group
Filtration by force through a semipermeable membrane
design is conceptually similar to the tubular module with a shell and tube arrangement. A single module can consist of 50 to thousands of hollow fibres
Ultrafiltration
Open source web server and a reverse proxy server
the addition of dynamic module loading. However, the modules still must be compiled at the same time as nginx, and not all modules are compatible with this
Nginx
Free software music tracker
for composing music in the MOD and XM module file formats. It is a clone that attempts to recreate the module replay and user experience of the popular
MilkyTracker
Interpretation of sensory information
of these modules take the form of sensory maps, mapping some aspect of the world across part of the brain's surface. These different modules are interconnected
Perception
German 155 mm self-propelled howitzer
developed by Krauss-Maffei Wegmann (now KNDS Deutschland). The RCH 155 Module takes the firepower and the range of the PzH 2000 by using its gun (155
RCH_155
In-development multiplayer space game
known as "modules", to provide players with the opportunity to experience gameplay features prior to release. The "Persistent Universe" module was made
Star_Citizen
identified with crossed modules, and are most often studied in that form. Thus, 2-groups in general can be seen as a weakening of crossed modules. Every 2-group
2-group
History of maths
properties such as a monoidal structure. 1949 John Henry Whitehead Crossed modules. 1949 André Weil Formulates the Weil conjectures on remarkable relations
Timeline of category theory and related mathematics
Timeline_of_category_theory_and_related_mathematics
or “make an earnest attempt to achieve.” Both the US Apollo 15's Lunar Module and a Space Shuttle were named Endeavour and accomplished bold discoveries
List of minor planets: 470001–471000
List_of_minor_planets:_470001–471000
American astronaut and lunar explorer (1930–2018)
then commanded the 1966 Gemini 10 mission. In 1969, he flew as command module pilot on Apollo 10, and became the first person to orbit the Moon alone
John_Young_(astronaut)
Industrial Automation Software
and FactoryPMI became the SQL Bridge Module and Vision Module, respectively. The Reporting Module and OPC-UA Module were included in the initial release
Inductive_Automation
Computer screensaver software
slider in the Flying Toasters module enabled users to adjust the toast's darkness, and an updated Flying Toasters Pro module added a choice of music—Richard
After_Dark_(software)
Malicious website exploit where unauthorized commands are transmitted from a trusted user
sent by untrusted sites to trusted ones. The Application Boundary Enforcer module in NoScript also blocks requests sent from internet pages to local sites
Cross-site_request_forgery
Mathematical structure
smash product is called a crossed product and denoted A ⋊ H {\displaystyle A\rtimes H} - not to be confused with the crossed product derived from C ∗ {\displaystyle
Group_Hopf_algebra
Army training program
the basic fundamentals of advanced special operations. Module J – MOS Cross Training: This module provides officers with knowledge and education of the
United States Army Special Forces selection and training
United_States_Army_Special_Forces_selection_and_training
Internal code for computer graphics
support that module's features, which are classified through capabilities, and declared early in the module. A validator can confirm that the module uses only
Standard Portable Intermediate Representation
Standard_Portable_Intermediate_Representation
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
List_of_gear_nomenclature
EDA/CAD software for creating schematic diagrams and printed circuit boards
delivers a number of features for visual and logical pin connections. Cross-module management ensures that principal circuits can be easily converted into
DipTrace
American astronaut (1930–2012)
Module (LM) pilot Buzz Aldrin became the first people to land on the Moon, and the next day they spent two and a half hours outside the Lunar Module Eagle
Neil_Armstrong
draft-ietf-spring-nsh-sr 0x92 146 Homa Homa transport protocol Homa research paper, HomaModule 0x93 147 BIT-EMU Bit-stream Emulation RFC 9801 0x94-0xFC 148-252 Unassigned
List_of_IP_protocol_numbers
Machine to increase pressure of gas by reducing its volume
next stage. Axial compressors are almost always multi-staged, with the cross-sectional area of the gas passage diminishing along the compressor to maintain
Compressor
Concept in aspect-oriented software development
aspect-oriented software development, cross-cutting concerns are aspects of a program that affect several modules, without the possibility of being encapsulated
Cross-cutting_concern
Baked item for Easter
arms crossed and hands placed on opposite shoulders. Hot cross buns are popular during Lent. The cross of course reminds the eater of Christ's cross. The
Hot_cross_bun
Argentine football player and manager (1960–2020)
rabona, a reverse-cross pass shot behind the leg that holds all the weight. This manoeuvre led to several assists, such as the cross for Ramón Díaz's header
Diego_Maradona
Open source web server
provided by modules, which are plugins that extend Caddy's configuration structure; for example, the HTTP server is a module. Caddy modules implement various
Caddy_(web_server)
Statistical Survey
http://www.gesis.org/issp/modules/ GESIS ISSP Modules by Year http://www.gesis.org/issp/modules/issp-modules-by-year/ GESIS ISSP Modules By Topic http://www
International Social Survey Programme
International_Social_Survey_Programme
Concept in cognitive psychology
A cognitive module in cognitive psychology is a specialized tool or sub-unit that can be used by other parts to resolve cognitive tasks. It is used in
Cognitive_module
Role-playing game published using the Open Game License
Dungeons & Dragons modules in content and style. The design ethos is summed up by the following statement included in every DCC module, regardless of which
Dungeon_Crawl_Classics
Spanish footballer (born 2007)
he also has the ability to play outswinging crosses to the far post. His ability to produce accurate crosses with the outside of his foot (known as a trivela)
Lamine_Yamal
Microwave network module
A phase shift module is a microwave network module which provides a controllable phase shift of the RF signal. Phase shifters are used in phased arrays
Phase_shift_module
from the planet's carbon dioxide atmosphere; China launched an unoccupied module containing living quarters for three crew members on a permanent space station
List of The Weekly with Charlie Pickering episodes
List_of_The_Weekly_with_Charlie_Pickering_episodes
Argentine footballer (born 1987)
pitch and curl shots on goal with his left foot, rather than predominantly cross balls for teammates. Under Guardiola and subsequent managers, he most often
Lionel_Messi
Indian lunar mission (2023–Present)
over the landing site, twelve days after landing. The orbiting propulsion module remained operational and was repurposed for scientific observations of Earth;
Chandrayaan-3
concludes the review by saying: "These psionicists are guys you don't want to cross." Swan, Rick (January 1995). "Role-playing Reviews". Dragon (#213). Lake
The_Will_and_the_Way_(module)
Web browser developed by Cliqz GmbH
Cliqz was a privacy-oriented web browser and search engine developed by Cliqz GmbH and majority-owned by Hubert Burda Media. It was available as a desktop
Cliqz
Modules used in early PDP computers
A DEC System Modules (originally known as System Building Blocks; the name was changed around 1961) are a DEC modular digital logic family which preceded
DEC_System_Module
Compiler that optimizes generated code
units which allows it to perform more aggressive optimizations like cross-module inlining and devirtualization. Machine code optimization involves using
Optimizing_compiler
International standard for mounting equipment
generally use "modules" as a width unit, one module being 18 mm wide. For example, a small device (e.g. a circuit breaker) may have a width of 1 module (18 mm
DIN_rail
Data interface description language
especially in cryptography. Protocol developers define data structures in ASN.1 modules, which are generally a section of a broader standards document written
ASN.1
British mathematician
Her first paper in homological algebra (Some algebraic properties of crossed modules) was published in 1951 and she earned her DPhil for her thesis Modern
Anne_Cobbe
Robot that can rearrange its own parts
self-reconfigurable module or collection of modules needs to possess. A matrix of modules does not need to be able to increase the quantity of modules in its matrix
Self-reconfiguring modular robot
Self-reconfiguring_modular_robot
Type of nuclear fission reactor
deliver an electrical power output as low as 10 MWe and up to 300 MWe per module. Reactors below 10 MWe in capacity are considered nuclear microreactors
Small_modular_reactor
Originally applied specifically to undocumented Mexican migrant workers who had crossed the United States border via the Rio Grande river to find work in the United
List_of_ethnic_slurs
Lack of confidence about one's way of speaking
Linguistic insecurity comprises feelings of anxiety, self-consciousness, or lack of confidence in the mind of speakers surrounding their use of language
Linguistic_insecurity
Building construction standard for positioning
surfaces, widths of shelves and kitchen components are multiples of the basic module. ISO 2848 is based on multiples of 300 mm and 600 mm. As dimensions increase
ISO_2848
Proposed Russian space station
Soviet space station project which began in February 1976. Some of the modules built for Mir-2 have been incorporated into the International Space Station
Mir-2
Lightweight programming language
values at run time), coroutines (cooperative multitasking) and dynamic module loading. The classic "Hello, World!" program can be written as follows,
Lua
Object-oriented framework for software development
into individual modules. With Qt 5.0 the architecture was modularized even further. Qt is now split into essential and add-on modules. Qt classes by default
Qt_(software)
Decoration for victorious generals of the Prussian Army and its allies
class of the Iron Cross, following the Star of the Grand Cross of the Iron Cross, which was awarded only twice. Along with the Iron Cross 1st and 2nd Class
Grand_Cross_of_the_Iron_Cross
Polish ice hockey player and footballer
Włodzimierz Lucjan Krygier (29 January 1900 – 17 September 1975) was a Polish ice hockey and football player. For hockey, he competed in the 1928 and 1932
Włodzimierz_Krygier
Programming language
A factorial algorithm implemented in Erlang: -module(fact). % This is the file 'fact.erl', the module and the filename must match -export([fac/1]). %
Erlang_(programming_language)
Scientific study of language
from one language to another in order to reach varied audiences. Cross-national and cross-cultural survey research studies employ translation to collect
Linguistics
Brown, Ronald; Spencer, Christopher B. (1976). "Double groupoids and crossed modules" (PDF). Cahiers de Topologie et Géométrie Différentielle Catégoriques
Elementary theory of abstract categories
Elementary_theory_of_abstract_categories
Borehole in Russia, deepest on Earth
international geophysical experiment obtained a reflection seismic crustal cross-section through the well. The Kola-92 working group consisted of researchers
Kola_Superdeep_Borehole
JavaScript runtime environment
using JavaScript and a collection of "modules" that handle various core functionalities.[excessive citations] Modules are provided for file system I/O, networking
Node.js
Indian Government COVID-19 vaccination portal
developed with five modules: the orchestration module; the vaccination cold chain module; the citizen registration module; the vaccinator module; and the certificate
CoWIN
water per day. The module comprises two identical treatment and supply lines, each provides water for 20,000 beneficiaries. The module weight about 11MT
Emergency Response Unit (IFRC)
Emergency_Response_Unit_(IFRC)
German symbol for skull and crossbones
wearing the traditional Stetson hat, and backed by either crossed cavalry sabers, crossed rifles, or some other variation, as an unofficial unit logo
Totenkopf
2025 aviation accident in India
incident aircraft's maintenance records showed that its throttle control module had been replaced in 2019 and 2023 for reasons unrelated to the fuel switches
Air_India_Flight_171
from diesels to gas turbines. The central module is matched to the engine driving it, the outer steering modules to the weight and speed of the vehicle.
Cross-drive steering transmission
Cross-drive_steering_transmission
Applies an electric current to heat or cool materials
effect). A thermoelectric module is made from three components: the conductors, the legs, and the substrate. Many of these modules are connected electrically
Thermoelectric_heat_pump
CROSSED MODULE
CROSSED MODULE
Boy/Male
British, English, Scandinavian
At the Cross
Surname or Lastname
English
English : variant of Cruse.Americanized spelling of German and Jewish Kraus.
Surname or Lastname
English
English : habitational name from either of two places in West Yorkshire named Crossley, from Old English cros ‘cross’ + lēah ‘woodland clearing’.
Boy/Male
English
Meadow with a Cross
Boy/Male
English
Meadow with a cross.
Surname or Lastname
English
English : unexplained. Perhaps a variant of Cripsey, habitational name from a place of this name in Lincolnshire.
Surname or Lastname
English
English : unexplained.Possibly an Americanized spelling of Swiss German Krüsi, a variant of Kruse, or Kriesi, a variant of Kries.
Surname or Lastname
English
English : topographic name for someone who lived near a stone cross set up by the roadside or in a marketplace, from Old Norse kross (via Gaelic from Latin crux, genitive crucis), which in Middle English quickly and comprehensively displaced the Old English form crūc (see Crouch). In a few cases the surname may have been given originally to someone who lived by a crossroads, but this sense of the word seems to have been a comparatively late development. In other cases, the surname (and its European cognates) may have denoted someone who carried the cross in processions of the Christian Church, but in English at least the usual word for this sense was Crozier.Irish : reduced form of McCrossen.In North America this name has absorbed examples of cognate names from other languages, such as French Lacroix.
Surname or Lastname
English
English : perhaps a habitational name (reduced form) from Costessey in Norfolk, named with an Old English or Old Norse personal name Cost + Old English ēg ‘island’, ‘dry ground in a marsh’.Americanized spelling of French Cossé (see Cosse).
Surname or Lastname
English
English : variant spelling of Cressy or possibly of Creasy.Probably also an altered spelling of German Kresse or Kresser.
Boy/Male
English
By the cross.
Boy/Male
Australian, French, Greek
Victorious; Crowned; Crucifixion; Cross
Male
Italian
Short form of Italian Crocifisso, or Croccifixio, CROSS means "cross; crucifix" or "way of the cross."
Surname or Lastname
English and French
English and French : variant spelling of Crozier.
Girl/Female
Spanish
Crowned.
Surname or Lastname
English and Irish
English and Irish : variant spelling of Cross.
Boy/Male
American, British, English
From the Cross Meadow
Boy/Male
Australian, Gaelic, Scottish
Headland
Surname or Lastname
German
German : habitational name from a place so named in East Prussia.English : possibly a variant spelling of Rosson.
Surname or Lastname
English
English : variant of Crossley, also established as a surname in Ireland.
CROSSED MODULE
CROSSED MODULE
Female
French
Feminine form of French Charles, CHARLINE means "man."
Girl/Female
Anglo Saxon
Sorrow.
Boy/Male
Tamil
Balgovind | பாலகோவிஂத
Lord Krishna
Boy/Male
English Scandinavian American
Medieval given name from Scandinavian mythology. Also English surname referring to a water crossing.
Girl/Female
Muslim
Gratitude, Gratefulness
Boy/Male
Hindu, Indian, Telugu
Son
Boy/Male
French
From the grassy plain.
Girl/Female
Indian
Women
Surname or Lastname
English
English : from Middle English starling ‘starling’ (Old English stærling), probably a nickname for a raucous or voracious person.
Boy/Male
Anglo Saxon
Present.
CROSSED MODULE
CROSSED MODULE
CROSSED MODULE
CROSSED MODULE
CROSSED MODULE
n.
A beam or bar across the head or end of a rod, etc., or a block attached to it and carrying a knuckle pin; as the solid crosspiece running between parallel slides, which receives motion from the piston of a steam engine and imparts it to the connecting rod, which is hinged to the crosshead.
a.
Incrusted; covered with, or containing, crust; as, old, crusted port wine.
a.
False; dishonest; fraudulent; as, crooked dealings.
a.
Crowded; compact; dense; pressed together.
a.
Clad or crowned with pine trees; as, pine-clad hills.
n.
A cross having the three upper ends crossed, so as to from three small crosses.
n.
A small cross.
a.
Crossed again; -- said of a cross the arms of which are crossed. SeeCross-crosslet.
n.
One who cross-examines or conducts a crosse-examination.
a.
Having the legs crossed.
a.
Having a crown shaped like a steeple; as, a steeple-crowned hat; also, wearing a hat with such a crown.
a.
Covered with hoarfrost or anything resembling hoarfrost; ornamented with frosting; also, frost-bitten; as, a frosted cake; frosted glass.
n.
A pilgrim bearing or wearing a cross.
a.
With arms crossed.
imp. & p. p.
of Cross
a.
Bearing a steeple; as, a steeple-crowned building.
v. t.
To make the sign of the cross upon; -- followed by the reflexive pronoun; as, he crossed himself.
n.
See Crosslet.
n.
The state of being closely surrounded, crowded, or pressed, as by ice.
a.
Crossed; intersected.