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Category theory lemma about commutative diagrams
In mathematics, the nine lemma (or 3×3 lemma) is a statement about commutative diagrams and exact sequences valid in the category of groups and any abelian
Nine_lemma
Lemma in category theory about commutative diagrams
Short five lemma, a special case of the five lemma for short exact sequences Snake lemma, another lemma proved by diagram chasing Nine lemma Massey (1991)
Five_lemma
Abhyankar's lemma Fundamental lemma (Langlands program) Five lemma Horseshoe lemma Nine lemma Short five lemma Snake lemma Splitting lemma Yoneda lemma Matrix
List_of_lemmas
Homological algebra statement
In homological algebra, the horseshoe lemma, also called the simultaneous resolution theorem, is a statement relating resolutions of two objects A ′ {\displaystyle
Horseshoe_lemma
Sequence of homomorphisms such that each kernel equals the preceding image
snake lemma shows how a commutative diagram with two exact rows gives rise to a longer exact sequence. The nine lemma is a special case. The five lemma gives
Exact_sequence
Theorem in queueing theory
In mathematical queueing theory, Little's law (also result, theorem, lemma, or formula) is a theorem by John Little which states that the long-term average
Little's_law
Group of mathematical theorems
S ∩ N is the meet. The third isomorphism theorem is generalized by the nine lemma to abelian categories and more general maps between objects. Below we
Isomorphism_theorems
Collection of maps which give the same result
include those typically given for the five lemma, the snake lemma, the zig-zag lemma, and the nine lemma. In higher category theory, one considers not
Commutative_diagram
Category with direct sums and certain types of kernels and cokernels
categories include the five lemma (and the short five lemma as a special case), as well as the snake lemma (and the nine lemma as a special case). An abelian
Abelian_category
Overview of and topical guide to category theory
Abelian category Exact sequence Exact functor Snake lemma Nine lemma Five lemma Short five lemma Mitchell's embedding theorem Injective cogenerator Derived
Outline_of_category_theory
Homological algebra is the study of homological functors
Differential module Five lemma Short five lemma Snake lemma Nine lemma Extension (algebra) Central extension Splitting lemma Projective module Injective
List of homological algebra topics
List_of_homological_algebra_topics
Theorem about inscribed and circumscribed circles
In geometry, the incenter–excenter lemma is the theorem that the line segment between the incenter and any excenter of a triangle, or between two excenters
Incenter–excenter_lemma
Category whose objects are groups and whose morphisms are group homomorphisms
categories, such as the nine lemma, the five lemma, and their consequences hold true in G r p {\displaystyle \mathbf {Grp} } . The snake lemma however is not true
Category_of_groups
Pair of integers related by their divisors
establish the theorem, Thâbit ibn Qurra proved nine lemmas divided into two groups. The first three lemmas deal with the determination of the aliquot parts
Amicable_numbers
Premier of New South Wales from 2005 to 2008
Retrieved 20 December 2010. "Failure to shoot straight derails Iemma". nineMSN. Archived from the original on 3 December 2007. "Anger good, swearing
Morris_Iemma
Representation of mechanical stress at every point within a deformed 3D object
internal surfaces. A consequence of Cauchy's postulate is Cauchy's Fundamental Lemma, also called the Cauchy reciprocal theorem, which states that the stress
Cauchy_stress_tensor
Intersection of triangle altitudes
stated in surviving Greek mathematical texts, but is used in the Book of Lemmas (proposition 5), attributed to Archimedes (3rd century BC), citing the "commentary
Orthocenter
Israeli mathematician
Perles–Sauer–Shelah lemma, a result in extremal set theory whose proof was credited to Perles by Saharon Shelah. The pumping lemma for context-free languages
Micha_Perles
Football league season
"Deportes Concepción anunció a Walter Lemma como su nuevo técnico" [Deportes Concepción announced Walter Lemma as their new manager] (in Spanish). Radio
2026_Liga_de_Primera
Palestinian photojournalist (born 1999)
from the original on 26 September 2024. Retrieved 18 May 2024. Shehadi, Lemma (16 May 2024). "'I lost my city': Gazan photographer Motaz Azaiza in tears
Motaz_Azaiza
leggere libri online (in Italian). Retrieved 13 February 2026. Tarekegn, Dr Lemma Nigatu; Mengistu, Mulu Getachew (10 November 2019). "Social Stigmatization
List_of_ethnic_slurs
Whole number
2016 at the Wayback Machine Cheng 2017, p. 32. Cheng 2017, pp. 41, 48–53. Lemma B.2.2, The integer 0 is even and is not odd, in Penner, Robert C. (1999)
0
American rapper
ended their rivalry and performed together on the same stage. "Kill Dash Nine" (appears on Rhyme Torrents Vol.1) Daniel "Monzy" Aminzade also created a
Dan_Maynes-Aminzade
Diagram that shows all possible logical relations between a collection of sets
Formal proof Formal semantics Foundations of mathematics Information theory Lemma Logical consequence Model Theorem Theory Type theory Theorems (list), paradoxes
Venn_diagram
List of films released by the home distribution company The Criterion Collection
considered part of the collection. The collection contains films from fifty-nine different countries, as well as several television miniseries. Films released
List of films in the Criterion Collection
List_of_films_in_the_Criterion_Collection
American filmmaker, photographer (1936–1984)
structural films that defined the movement, including Lemon (1969), Zorns Lemma (1970), and Hapax Legomena (1971–1972), as well as his anthology book, Circles
Hollis_Frampton
List of terms used in biology
adjectives vary in spelling according to gender, and in most cases only the lemma form (nominative singular masculine form) is listed here. 1st-and-2nd-declension
List of Latin and Greek words commonly used in systematic names
List_of_Latin_and_Greek_words_commonly_used_in_systematic_names
South African politician (born 1964)
2025.{{cite news}}: CS1 maint: deprecated archival service (link) Shehadi, Lemma (4 June 2024). "Nelson Mandela adviser sees united struggle as he runs against
Andrew_Feinstein
Ethnic group
Dicționarul etimologic român (in Romanian), quoted in DEX-online (see lemma rudár (sing.), rudári (pl.) followed by both definitions: "gold-miner" and
Romani_people
Digital library of Tufts University
readers to look for a text by its author or the presence of a specific lemma or word. Perseus also enhanced its texts through TEI-compliant markup language
Perseus_Digital_Library
Theorem in combinatorics
is smaller than its domain". Advanced mathematical proofs like Siegel's lemma build upon this more general concept. Dirichlet published his works in both
Pigeonhole_principle
Country in Northern Europe
etymologisk ordbok [Swedish etymological dictionary] (in Swedish). Gleerup. Lemma: SWEDEN Archived 20 April 2021 at the Wayback Machine, Instituut voor de
Sweden
American actor (born 1951)
Hodder and Bill Oberst in 2022. He starred as, Captain Harris, in all 5 Ice Nine Kills music videos for their 2021 horror film-themed album The Silver Scream
Bill_Moseley
Mythological human able to transform into a wolf
discovered as of May 2025 that Simeon I of Bulgaria had a son named Bajan. Lemma: Weerwolf, Instituut voor de Nederlandse Taal (in Dutch) Orel 2003, p. 463
Werewolf
Mathematics of number-placement puzzle
solutions is then the number of orbits, which can be computed using Burnside's lemma. The Burnside fixed points are grids that either do not change under the
Mathematics_of_sudoku
Concept in linguistics
Triantaphyllide online dictionary, Greek Language Center (Kentro Hellenikes Glossas), lemma Franc ( Φράγκος Phrankos), Lexico tes Neas Hellenikes Glossas, G.Babiniotes
Lingua_franca
Biblical character
unnamed prophet is mentioned in Isaiah. "Huldah" derives from the Hebrew lemma חלד (Ḥ-L-D), meaning to abide or to continue. The Huldah Gates in the Southern
Huldah
and the theory of Sturmian words. Noether normalization lemma The Noether normalization lemma is a result of commutative algebra, introduced by Emmy Noether
List of inventions and discoveries by women
List_of_inventions_and_discoveries_by_women
17th-century conjecture proved by Andrew Wiles in 1994
proof contained a major gap. However, since Euler himself had proved the lemma necessary to complete the proof in other work, he is generally credited
Fermat's_Last_Theorem
Championship-style competition
WMM, Abbott World Marathon Majors announced that they would create a new Nine Star medal for the expanded race series. As of the completion of the London
World_Marathon_Majors
American television host and writer (born 1949)
Archived from the original on February 24, 2015. Retrieved February 24, 2015. Lemma, Ingrid (September 26, 2009). "VVH-TV's "American Dreams Show"" (Interview)
Bill O'Reilly (political commentator)
Bill_O'Reilly_(political_commentator)
German polymath and scholar (1777–1855)
some key arithmetic concepts, such as Fermat's little theorem and Gauss's lemma. The main objective of introducing this ring was to formulate the law of
Carl_Friedrich_Gauss
Country in Southeast Asia
while Ngô Bảo Châu won the 2010 Fields Medal for his proof of fundamental lemma in the theory of automorphic forms. Since the establishment of the Vietnam
Vietnam
Italian media tycoon and politician (1936–2023)
2013. Floriano De Angeli, "L'Europeo", n. 49, 1993 "berlusconismo" s. m., lemma del Vocabolario Treccani online, dal sito dell'Istituto dell'Enciclopedia
Silvio_Berlusconi
Field of mathematics and science based on non-linear systems and initial conditions
Patterns in nature Predictability Quantum chaos Santa Fe Institute Shadowing lemma Synchronization of chaos Unintended consequence People Ralph Abraham Michael
Chaos_theory
Online encyclopedia founded by Larry Sanger
2016. As of 21 July 2023[update], it had 17,956 "live" and 6,322 "lemma" articles (lemmas are undeveloped articles that contain little more than a definition
Citizendium
Branch of pure mathematics
A fundamental property of primes is shown in Euclid's lemma. It is a consequence of the lemma that if a prime divides a product of integers, then that
Number_theory
Number divisible only by 1 and itself
proofs of the uniqueness of prime factorizations are based on Euclid's lemma: If p {\displaystyle p} is a prime number and p {\displaystyle p}
Prime_number
Short Films Competition Absent Noksan Cem Demirer Turkey Alazar Beza Hailu Lemma Ethiopia, France, Canada Dancing in the Corner Taniec w Narożniku Jan Bujnowski
2024_Cannes_Film_Festival
Relation between sides of a right triangle
normal to their common base, connecting the parallel lines BD and AL. (lemma 2) Since C is collinear with A and G, and this line is parallel to FB, then
Pythagorean_theorem
Largest city and administrative center of Primorsky Krai, Russia
classic and modern rock music, oldies and music of the 1980s–1990s. Radio Lemma (FM 102,7 MHz, since 1996) broadcasts news, radio shows and various Russian
Vladivostok
and Markov processes. The Dynkin diagram, the Dynkin system, and Dynkin's lemma are named after him. Paul Ehrenfest (1880–1933): Austrian and Dutch theoretical
List of atheists in science and technology
List_of_atheists_in_science_and_technology
"Statistics". Wiktionary. Retrieved March 10, 2026. "Category:English lemmas". en.wiktionary.org. June 20, 2022. Archived from the original on March
List of dictionaries by number of words
List_of_dictionaries_by_number_of_words
Algorithm for computing greatest common divisors
must also divide the left-hand side, v. This result is known as Euclid's lemma. Specifically, if a prime number divides L, then it must divide at least
Euclidean_algorithm
Major river in northeast Africa
8644, section 3.5.4. Lemma 2019, p. 1. Talbot & Williams 2009, p. 38. Talbot & Williams 2009, p. 37. Sutcliffe 2009, p. 359. Lemma 2019, p. 11. Senay 2014
Nile
North Germanic language
swapped, or ablauted, in the nucleus of a word. Strong verbs ablaut the lemma's nucleus to derive the past forms of the verb. This parallels English conjugation
Old_Norse
Chilean football club
Cornejo [es] (2024) Manuel Suárez (2024-2025) Patricio Almendra (2025-2026) Walter Lemma (2026) Alejandro Gutiérrez (2026) Fernando Díaz (2026-) Seasons in Primera
Deportes_Concepción_(Chile)
Phonology of the English language
syllable ending in an unreduced short vowel, this is avoided. Thus the word lemma should be divided /ˈlɛm.ə/ and not */ˈlɛ.mə/, even though the latter division
English_phonology
Persian polymath and poet (1048–1131)
that Saccheri "used the same lemma as the one of Tusi, even lettering the figure in precisely the same way and using the lemma for the same purpose". He
Omar_Khayyam
Comune in Trentino-Alto Adige/Südtirol, Italy
Die Ortsnamen Südtirols, Vol. 1 (2000), lemma Meran Johann Jacob Hofmann, Lexicon Universale (1698), lemma 'Tirolis' "Museum Burg Hasegg/Münze Hall in
Merano
Criminal organization in Italy
Henry George; Scott, Robert; A Greek–English Lexicon at the Perseus Project lemma ανδραγαθία; Babiniotis, Georgios. Dictionary of Modern Greek. Athens: Lexicology
'Ndrangheta
Species of grass
nine-nerved. The lemmas are 7.5–9 mm (0.3–0.4 in) long and 1.9–2.5 mm (0.07–0.10 in) wide, with seven to nine visible, conspicuous nerves. The lemmas
Bromus_hordeaceus
Series of demonstrations since 2023
2023.{{cite news}}: CS1 maint: deprecated archival service (link) Shehadi, Lemma (19 November 2023). "UK charities urge Rishi Sunak to call for ceasefire
Gaza war protests in the United Kingdom
Gaza_war_protests_in_the_United_Kingdom
Greek goddess of the harvest, grains, and agriculture
of the Hellenic World: Asia Minor. http://asiaminor.ehw.gr/Forms/fLemmaBody.aspx?lemmaId=10541#noteendNote_11 Apuleius (1998). The Golden Ass. Penguin classics
Demeter
Ancient Egyptian god of the Earth
spell the name of the god (H.te Velde, in: Lexikon der Aegyptologie II, lemma: Geb). An alternative ancient name for this goose species was trp meaning
Geb
German mathematician (1885–1955)
Weyl–Schouten theorem Weyl's criterion (disambiguation) Weyl's lemma on hypoellipticity Weyl's lemma on the "very weak" form of the Laplace equation Weyl, H
Hermann_Weyl
State-owned airline of Ethiopia
lounges at Bole International Airport. Cloud Nine passengers can wait for the departure of flights at the Cloud Nine Lounge, where they are provided with a
Ethiopian_Airlines
Mathematician and astronomer (1473–1543)
his heliocentric models. Copernicus used what is now known as the Urdi lemma and the Tusi couple in the same planetary models as found in Arabic sources
Nicolaus_Copernicus
Extinct Indo-European language in Asia
Krause; Werner Thomas (1960). Tocharisches Elementarbuch: Grammatik (in German). Vol. 1. Carl Winter. Retrieved 2025-05-11. Tocharian A lemmas in Wiktionary
Tocharian_A
Practice and study of secure communication techniques
protected as free speech by the United States Constitution. In 1996, thirty-nine countries signed the Wassenaar Arrangement, an arms control treaty that deals
Cryptography
Computation model defining an abstract machine
have allowed all nine possible types of five-tuples: Any Turing table (list of instructions) can be constructed from the above nine 5-tuples. For technical
Turing_machine
Ancient Egyptian city located in present-day Ayn Shams, Cairo
Antiquities (Al-maǧlis al-aʿlá li-l-aṯār). p. 496. ISBN 9773053474. TLA lemma no. C5494 (ⲱⲛ), in: Coptic Dictionary Online, ed. by the Koptische/Coptic
Heliopolis_(ancient_Egypt)
Polynomial equation of degree 3
left-hand side is the product of polynomials of lower degrees. By Gauss's lemma, if the equation is reducible, one can suppose that the factors have integer
Cubic_equation
Geometry theorem
are Lemmas VIII, XII, XIII, XV, and XVII in the part of Book VII consisting of lemmas to the first of the three books of Euclid's Porisms. Lemma VIII
Pappus's_hexagon_theorem
Island county in Wales
Indogermanisches Etymologisches Wörterbuch: Record number 1277 (Root / lemma: men-1) "Local Food Heroes on Anglesey". greentraveller.co.uk. 18 April
Anglesey
Arithmetic operation
doi:10.1016/j.jnt.2008.10.018. Jacob Fox, A new proof of the graph removal lemma, arXiv preprint (2010). arXiv:1006.1300 [math.CO] Daniel Geisler, Tetration
Tetration
Overview of how Japanese verbs conjugate
to which inflectional suffixes attach. The "default" dictionary form, or lemma, of any conjugational morpheme, be it a verb, an adjective or an auxiliary
Japanese_conjugation
Right to participate in one's own governance
McGill-Queen's Press - MQUP. pp. 106–108. ISBN 978-0-7735-0383-0. Sardismo, lemma, Garzanti Linguistica. Pala, C. 2015. Sardinia. The Wiley Blackwell Encyclopedia
Self-determination
Circles tangent to all three sides of a triangle
Harcourt's theorem – Formula for the area of a triangle Incenter–excenter lemma – Theorem about inscribed and circumscribed circles Inscribed sphere – Sphere
Incircle_and_excircles
Polish-American mathematician (1900–1992)
achieved in collaboration with Calderón. In particular, the Calderón–Zygmund lemma is regarded as a fundamental result in this area of mathematics. It was
Antoni_Zygmund
Non-orientable surface with one edge
S2CID 122209943. Mangahas, Johanna (July 2017). "Office Hour Five: The Ping-Pong Lemma". In Clay, Matt; Margalit, Dan (eds.). Office Hours with a Geometric Group
Möbius_strip
Category of words based on shared grammatical properties in a clause
relating to English vocabulary organized by part of speech, see the English lemmas category of words in Wiktionary, the free dictionary. Media related to Parts
Part_of_speech
British barrister and life peer (born 1968)
for weeks". The Times. Retrieved 30 July 2024. Harding, Thomas; Shehadi, Lemma. "British Attorney General travels to Israel as arms ban threat rises".
Richard_Hermer,_Baron_Hermer
Russian mathematician (1937–2008)
1 , … , r {\displaystyle s=1,\dots ,r} . The mean value theorem and the lemma on the multiplicity of intersection of multi-dimensional parallelepipeds
Anatoly_Karatsuba
About simultaneous modular congruences
the proofs (except for the first existence proof), are based on Euclid's lemma and Bézout's identity, which are true over every principal domain. However
Chinese_remainder_theorem
System of formal deduction in logic
rules that characterise that logic. We describe here a Hilbert system with nine axioms and just the rule modus ponens, which we call the one-rule axiomatisation
Hilbert_system
Branch of elementary mathematics
ISBN 978-1-4994-7092-5. Rossi, Richard J. (2011). Theorems, Corollaries, Lemmas, and Methods of Proof. John Wiley & Sons. ISBN 978-1-118-03057-8. Ruthven
Arithmetic
German mathematician (1882–1935)
his work in group theory, particularly Fitting's theorem and the Fitting lemma. He died at the age of 31 of a bone disease. Witt was initially supervised
Emmy_Noether
363, 364, ISBN 0-7864-2248-3; compare Suiones. Pokorny, Julius. "Root/Lemma se-". Indogermanisches Etymologisches Wörterbuch. Indo-European Etymological
List of etymologies of administrative divisions
List_of_etymologies_of_administrative_divisions
Polyhedron with 9 faces
Theory, 9 (1): 54–59, doi:10.1016/S0021-9800(70)80054-0. By the handshaking lemma, a face-regular polyhedron with an odd number of faces must have faces with
Enneahedron
Counterintuitive result in probability
one of these strings. Both follow easily from the second Borel–Cantelli lemma. For the second theorem, let Ek be the event that the kth string begins
Infinite_monkey_theorem
grasp, seize, take Greek λαμβάνειν (lambánein), λῆψις (lêpsis), λῆμμα (lêmma) analemma, analemmatic, analeptic, catalepsy, cataleptic, dilemma, dilemmatic
List of Greek and Latin roots in English/H–O
List_of_Greek_and_Latin_roots_in_English/H–O
Set of words
equates words with lemmas (the inflected or dictionary form; this includes walk, but not walks, walked or walking). Most of the time lemmas do not include
Vocabulary
Gernaey, Angela M.; Galili, Ehud; Eshed, Vered; Greenblatt, Charles L.; Lemma, Eshetu; Bar-Gal, Gila Kahila; Spigelman, Mark (2008). "Detection and molecular
History_of_tuberculosis
progressed significantly, and there have been proofs of the fundamental lemma (2008), as well as a proposed proof of the geometric Langlands correspondence
History_of_mathematics
Discrete (i.e., incremental) version of infinitesimal calculus
triangulations (barycentric subdivision, dual triangulation), Poincaré lemma, the first proof of the general Stokes Theorem, and a lot more L. E. J.
Discrete_calculus
Imperial bodyguards of Ethiopia
Brigadier-General Mengistu Neway (April 1956 – 13 December 1960) Major-General Tafessa Lemma (1974) Abebe Bikila, professional athlete and member of the 5th Infantry
Kebur_Zabagna
Standard system of axiomatic set theory
Y)\right]\right].} A third version of the axiom, also equivalent, is Zorn's lemma. Since the existence of a choice function when X {\displaystyle X} is a
Zermelo–Fraenkel_set_theory
April 2020. lemma-follows-in-the-footsteps-of-bastion-mirrors-edge Archived 2016-12-30 at the Wayback Machine on Rock, Paper, Shotgun (2014) lemma-first-person-parkour
List of commercial video games with later released source code
List_of_commercial_video_games_with_later_released_source_code
Sequence of characters that forms a search pattern
language of squares is not regular, nor is it context-free, due to the pumping lemma. However, pattern matching with an unbounded number of backreferences, as
Regular_expression
travel, tourism, insurance
NINE LEMMA
NINE LEMMA
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NINE LEMMA
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travel, tourism, insurance