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Lemma in category theory about commutative diagrams
abelian category theory, the five lemma is an important and widely used lemma about commutative diagrams. The five lemma is valid for all abelian categories
Five_lemma
Special case of the five lemma
other applications of abelian category theory, the short five lemma is a special case of the five lemma. It states that for the following commutative diagram
Short_five_lemma
Sequence of homomorphisms such that each kernel equals the preceding image
is an isomorphism; the short five lemma is a special case thereof applying to short exact sequences. The importance of short exact sequences is underlined
Exact_sequence
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
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
Category with direct sums and certain types of kernels and cokernels
short exact sequences, and derived functors. Important theorems that apply in all abelian categories include the five lemma (and the short five lemma
Abelian_category
Group for which a given group is a normal subgroup
the map T {\displaystyle T} is forced to be an isomorphism by the short five lemma. It may happen that the extensions 1 → K → G → H → 1 {\displaystyle
Group_extension
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
Type of pumping lemma
formal language theory, the pumping lemma for context-free languages, also known as the Bar-Hillel lemma, is a lemma that gives a property shared by all
Pumping lemma for context-free languages
Pumping_lemma_for_context-free_languages
Every graph has evenly many odd vertices
In graph theory, the handshaking lemma is the statement that, in every finite undirected graph, the number of vertices that touch an odd number of edges
Handshaking_lemma
Branch of mathematical logic
theory such as the classical theorem that the axiom of choice and Zorn's lemma are equivalent over ZF set theory. The goal of reverse mathematics, however
Reverse_mathematics
Mathematical group with trivial abelianization
the classification theorem. A basic fact about perfect groups is Grün's lemma (Grün 1935, Satz 4, p. 3), due to Otto Grün: the quotient of a perfect group
Perfect_group
Large geographical region identified by convention
lemma continent (epeiros), 5 continents model; Lexico Triantaphyllide online dictionary, Greek Language Center (Kentro Hellenikes Glossas), lemma continent
Continent
Homological algebra is the study of homological functors
complex 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
Combinatorial and geometric result used in measure theory of Euclidean spaces
the Vitali covering lemma is a combinatorial and geometric result commonly used in measure theory of Euclidean spaces. This lemma is an intermediate step
Vitali_covering_lemma
Branch of mathematics
of vector spaces over a given field) or in the category of groups. The five lemma states that, if the rows are exact, m and p are isomorphisms, l is an
Homological_algebra
Algebraic topology uses abstract algebra to study topological spaces
Chain complex Commutative diagram Exact sequence Five lemma Short five lemma Snake lemma Splitting lemma Extension problem Spectral sequence Abelian category
List of algebraic topology topics
List_of_algebraic_topology_topics
Ethiopian artist (1928–2020)
Lemma Guya Gemeda (Oromo: Lammaa Guyyaa Gammadaa; 13 February 1928 – 26 October 2020) was an Ethiopian painter, airplane pilot, and author. He created
Lemma_Guya
Premier of New South Wales from 2005 to 2008
it had enjoyed under Carr, despite Iemma's relatively low profile. His short-term position was improved by the sudden resignation of Liberal leader John
Morris_Iemma
Geometric treatise on circles attributed to Archimedes
The Book of Lemmas or Book of Assumptions (Arabic Maʾkhūdhāt Mansūba ilā Arshimīdis) is a book attributed to Archimedes by Thābit ibn Qurra, though the
Book_of_Lemmas
British mathematician
In 2003, Gowers established a regularity lemma for hypergraphs, analogous to the Szemerédi regularity lemma for graphs. In 2005, he introduced the notion
Timothy_Gowers
Identity in analytic number theory
of Mathematics, EMS Press Heath-Brown, D. R. (1982), "Prime numbers in short intervals and a generalized Vaughan identity", Can. J. Math., 34 (6): 1365–1377
Vaughan's_identity
Euler's formula Euler's four-square identity Euler's theorem Five color theorem Five lemma Fundamental theorem of arithmetic Gauss–Markov theorem (brief
List_of_mathematical_proofs
How often each letter appears in written language
used in the chart below, is to count letter frequency in lemmas of a dictionary. The lemma is the word in its canonical form. The second method is to
Letter_frequency
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
Condition under which an odd prime is a sum of two squares
theorem Lagrange's four-square theorem Landau–Ramanujan constant Thue's lemma Friedlander–Iwaniec theorem D. A. Cox (1989). Primes of the Form x2 + ny2
Fermat's theorem on sums of two squares
Fermat's_theorem_on_sums_of_two_squares
Collection of maps which give the same result
chasing 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
Commutative_diagram
Prime Minister of Ethiopia since 2018
Ethiopian constitution. Therefore, Lemma Megersa was excluded from the leadership race. On 22 February 2018, Lemma Megersa's party, ODP, called for an
Abiy_Ahmed
American killer (born 1998)
writing, "Clearly written by a mathematics prodigy. Reads like a series of lemmas on the question of 21st-century quality of life", and "It's easy to quickly
Luigi_Mangione
Genus of grasses
with reduced upper florets. The lemma tips have between two and five teeth. Described in 1886, the genus contains five species native to California and
Orcuttia
Every positive integer is a sum of at most n n-gonal numbers
Cauchy in 1813. The proof of Nathanson (1987) is based on the following lemma due to Cauchy: For odd positive integers a and b such that b2 < 4a and 3a
Fermat polygonal number theorem
Fermat_polygonal_number_theorem
One of several theorems in different areas of mathematics
infinite. Schur's lemma (Riemannian geometry) Heule, Marijn J. H. (2017). "Schur Number Five". arXiv:1711.08076 [cs.LO]. "Schur Number Five". www.cs.utexas
Schur's_theorem
Musical interval
diapason (Greek for "across all"). 3/2 is the perfect fifth, diapente ("across five"), or sesquialterum. 4/3 is the perfect fourth, diatessaron ("across four")
Pythagorean_interval
hypotheses List of inequalities Lists of integrals List of laws List of lemmas List of limits List of logarithmic identities List of mathematical functions
List_of_theorems
In mathematics, a statement that has been proven
qualify as theorems only the most important results, and use the terms lemma, proposition and corollary for less important theorems. In mathematical
Theorem
Area of combinatorics
always mark at least one-third of them. Extremal graph theory Sauer–Shelah lemma Erdős–Ko–Rado theorem Kruskal–Katona theorem Fisher's inequality Union-closed
Extremal_combinatorics
Spectral sequence
-acyclic. Hence, the hypothesis is satisfied. We shall use the following lemma: Lemma—If K is an injective complex in an abelian category C such that the kernels
Grothendieck spectral sequence
Grothendieck_spectral_sequence
Study of flower structures
formed by the lemma, attached to the rachilla and the palea inserted on the floral axis that arises above the rachilla in the axil of the lemma and supports
Floral_morphology
Visual representation of a mathematical relationship
left-justified rows, with the row sizes weakly decreasing (each row has the same or shorter length than its predecessor). Listing the number of boxes in each row gives
Mathematical_diagram
Lexical core of a word without affixes
lexical endings in place. For example, chatters has the inflectional root or lemma chatter, but the lexical root chat. Inflectional roots are often called
Root_(linguistics)
List of terms used in biology
genus). Adjectives vary 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
1998 mathematics book by Aigner and Ziegler
Chapter 24: Van der Waerden's conjecture. Chapter 25: Littlewood–Offord lemma. Chapter 26: The cotangent and Herglotz's trick. Chapter 27: Buffon's needle
Proofs_from_THE_BOOK
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
American computer scientist
pseudorandom number generator from any one-way function, his proof of Yao's XOR lemma via "hard core sets", his proof of the exponential size lower bound for
Russell_Impagliazzo
Process by which people translate thoughts into verbal words
short sentences (telegraphic phase). After two and a half years, the infant develops systems of lemmas used in speech production. Around four or five
Speech_production
Statement in mathematical combinatorics
either case the proof is complete. Lemma 1 implies that any R(r,s) is finite. The right hand side of the inequality in Lemma 2 expresses a Ramsey number for
Ramsey's_theorem
French mathematician (1875–1941)
series, that the nth Fourier coefficient tends to zero (the Riemann–Lebesgue lemma), and that a Fourier series is integrable term by term. In 1904-1905 Lebesgue
Henri_Lebesgue
Species of flowering plant
nutritionix.com. 22 February 2016. Retrieved 2025-10-23. Harold H. Lee, Lemma Aklilu, and Harriett J. Bennett, 1992, The use of Endod (Phytolacca dodecandra)
Phytolacca_americana
Cell membrane of a muscle fibre
The sarcolemma (sarco (from sarx) from Greek; flesh, and lemma from Greek; sheath), also called the myolemma, is the cell membrane surrounding a skeletal
Sarcolemma
Game of strategy
from these two lemmas. Lemma 1. If s = 0, then t ≠ 0 no matter what move is made. Proof: If there is no possible move, then the lemma is vacuously true
Nim
Loss of precision in numerical analysis
enough, the floating-point difference is computed exactly, by the Sterbenz lemma—there is no rounding error introduced by the floating-point subtraction
Catastrophic_cancellation
Matoušek (2002), Lemma 5.4.2, p. 97; Matoušek (2003), Lemma 1.6.4, p. 17. Gale (1963); Edelsbrunner (1987), p. 101; Matoušek (2002), Lemma 5.4.2, p. 97.
Moment_curve
Basis for Euclidean geometry
of the five groups of axioms. In other words, the elements of geometry form a system which is not susceptible of extension, if we regard the five groups
Hilbert's_axioms
Volume of a sound or note
via YouTube. Ferneyhough, Brian (1982). Lemma-Icon-Epigram. London: Edition Peters 7233. Brian Ferneyhough - Lemma-Icon-Epigram (w/ score) (for piano solo)
Dynamics_(music)
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
Species of grass
cultivation. The grain is also optimal for storage due to the tight coating of lemma and palea. The crop is grown around the world for various uses, however
Echinochloa_esculenta
American investor
equity funds such as Fidelity Investments Fidelity Contrafund (FCNTX) and Lemma Senbet Fund, to index funds such as Russell Indexes iShares Russell 1000
Peter_Lynch
British politician
MP for Sheffield". Yorkshire Bylines. Retrieved 16 July 2024. Shehadi, Lemma (5 July 2024). "Abtisam Mohamed becomes first Yemeni elected as British
Abtisam_Mohamed
Austrian-American mathematician (1921-2002)
functional analysis, and differential geometry. He is known for Mautner's Lemma and Mautner's Phenomenon in the representation theory of Lie groups. Following
Friederich_Ignaz_Mautner
River in Central Africa
Ocean. p. 112. Congo River, called Zahir or Zaire by the natives Hanibal Lemma, and colleagues (2019). "Bedload transport measurements in the Gilgel Abay
Congo_River
American mathematician (1892–1977)
technique of differential topology now known as Morse theory. The Morse–Palais lemma, one of the key results in Morse theory, is named after him, as is the Thue–Morse
Marston_Morse
Hungarian-American mathematician
computer science, including Szemerédi's theorem, the Szemerédi regularity lemma, the Erdős–Szemerédi theorem, the Hajnal–Szemerédi theorem and the Szemerédi–Trotter
Endre_Szemerédi
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
Self-describing sentence
3's, 3 4's, 1 5, 2 6's, 1 7, 2 8's, and 1 9. Quine (computing) Diagonal lemma Sallows, L., In Quest of a Pangram, Abacus, Vol 2, No 3, Spring 1985, pp
Autogram
Surjective ring homomorphism with a given codomain
algebra homomorphism E → E' that induces the identities on I and R. By the five lemma, such a morphism is necessarily an isomorphism, and so two extensions
Algebra_extension
Authenticated encryption mode for block ciphers
the success probability in observation 1 of this paper matches that of lemma 2 from the INDOCRYPT 2004 analysis (setting w = 128 and l = n × 128). Saarinen
Galois/Counter_Mode
Species of grass
than the spikelets and thinner than fertile lemmas. Both upper and lower glumes are lanceolate. Fertile lemmas are 10 to 12 mm (3⁄8 to 1⁄2 in) long with
Bromus_berteroanus
Theorem in projective geometry
transformation. This was realised by Pascal, whose first lemma states the theorem for a circle. His second lemma states that what is true in one plane remains true
Pascal's_theorem
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
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
Dutch encyclopedia
and consists of 20 volumes A-Z, and four index volumes with references to lemmas within the treated subjects. The fourth index volume also contains a comprehensive
Grote_Spectrum_Encyclopedie
Long dense subsets of the integers contain arbitrarily large arithmetic progressions
Arithmetic combinatorics Szemerédi regularity lemma Van der Waerden's theorem Hypergraph removal lemma § Proof of Szemerédi's theorem Erdős, Paul; Turán
Szemerédi's_theorem
Wife of Odysseus in Greek mythology
(in Greek). Translated by C. Roy, R. S. Smith. 2026. Γλῶσσαι. Zeno.org lemma Archived 2008-12-11 at the Wayback Machine relating πηνέλωψ (gen. πηνέλοπος)
Penelope
Municipality in Catalonia, Spain
from the original on 16 March 2016. Retrieved 13 July 2016. A. Lambert, lemma 'Barcelone', in Dictionnaire d'Histoire et de Géographie ecclésiastiques
Terrassa
Mountain in Italy
Cime di Lemma is a 2,348-metre (7,703 ft) mountain peak of Lombardy, Italy. It is located within the Bergamo Alps, near the border of the provinces of
Cime_di_Lemma
American computer scientist (born 1946)
already as an undergraduate published a research paper about Sperner's lemma, which he learned about from Hans Rademacher. He completed his doctorate
Daniel_I._A._Cohen
from 2016, came here as the alternate filling the shoes of injured Sisay Lemma. Abdi was also bronze medalist in 2022. 2023 World Champion Victor Kiplangat
Athletics at the 2024 Summer Olympics – Men's marathon
Athletics_at_the_2024_Summer_Olympics_–_Men's_marathon
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
County in Florida, United States
of Seminole County. As of 2022[update] the current sheriff is Dennis M. Lemma, who took office in 2017. The Seminole County Sheriff's Office is currently
Seminole_County,_Florida
1979 conjecture in combinatorics
system is union-closed if and only if its complement is intersection-closed. Lemma 1. If X {\displaystyle X} is a union-closed family of sets with universe
Union-closed_sets_conjecture
Palm. Out of 4.420 entries, the following eleven short films were selected to compete for the Short Film Palme d'Or: The Cinéfondation (or La Cinéf) section
2024_Cannes_Film_Festival
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
On rays from a point to a line, with equal inscribed circles between adjacent rays
the hyperbolic sine. The theorem is a direct corollary of the following lemma: Suppose that the nth ray makes an angle γ n {\displaystyle \gamma _{n}}
Equal_incircles_theorem
Ethiopian television network
minister. In February 2018, the president of the Oromia regional state, Lemma Megersa, pledged to defend the independence and impartiality of the state-run
Oromia_Broadcasting_Network
Phonology of the English language
in the preceding syllable ending in an unreduced short vowel, this is avoided. Thus the word lemma should be divided /ˈlɛm.ə/ and not */ˈlɛ.mə/, even
English_phonology
Species of plant
flowered panicles often reach heights of five feet. The spikelets consist of a single awnless floret with a 3-nerved lemma. The native range of the grass extends
Muhlenbergia_rigens
British-Canadian codebreaker and mathematician (1917–2002)
impulses, and it was established that the five chi wheels all advanced with each new character and that the five psi wheels all moved together under the
W._T._Tutte
Type of topological space
This is a stronger separation property than normality, as by Urysohn's lemma disjoint closed sets in a normal space can be separated by a function, in
Normal_space
18 mathematical problems stated in 1998
doi:10.3390/analytics1010003. Asaoka, M.; Irie, K. (2016). "A C∞ closing lemma for Hamiltonian diffeomorphisms of closed surfaces". Geometric and Functional
Smale's_problems
41st annual marathon race in London
chances of a mass participation event. The elite events were won by Sisay Lemma of Ethiopia and Joyciline Jepkosgei of Kenya, in 2:04:01 and 2:17:43, respectively
2021_London_Marathon
Functional programming language
(suc (suc zero)) lemma2 = check-even-tactic auto The actual proof of each lemma will be automatically constructed at type-checking time. If the tactic fails
Agda_(programming_language)
American mathematical physicist
as rearrangement inequalities or the Brezis-Lieb lemma which provides the missing term in Fatou's lemma for sequences of functions converging almost everywhere
Elliott_H._Lieb
Species of grass
long, arising 0.4–1.2 mm (0.016–0.047 in) below the lemma. The paleas are shorter than the lemmas, with glabrous backs and ciliate keels. The dark brown
Bromus_hordeaceus
Championship-style competition
(second) and $10,000 (third). The World Marathon Majors began in 2006 with five races: Berlin, Boston, Chicago, London, and New York. The Tokyo Marathon
World_Marathon_Majors
Mathematics optimization problem
algorithm relies on "Lemma 1" proved in a 1981 technical report and omitted from the published paper. The technical report's proof of the lemma is incorrect,
Matrix_chain_multiplication
Chitwood, Volusia County Sheriff Grady Judd, Polk County sheriff Dennis Lemma, Seminole County Sheriff Cory Mills Executive branch officials Donald Trump
2026 United States House of Representatives elections in Florida
2026_United_States_House_of_Representatives_elections_in_Florida
Deity of Shinto religion
origin of the verb is suggested to be a precursor to the Middle Korean lemma yènc- meaning 'to place/put on [the top of]' reconstructed as *yenc-a (place-INF)
Izanagi
Species of shrub
scientists - and may be effective controlling schistosomiasis. After Aklilu Lemma, an Ethiopian scientist, demonstrated endod's potency to American scientists
Phytolacca_dodecandra
Recursive integer sequence
{2n+1}{n}}\,,} which can be directly interpreted in terms of the cycle lemma; see below. The Catalan numbers satisfy the recurrence relations C 0 = 1
Catalan_number
Quality of zero being an even number
explained by the degree sum formula. Sperner's lemma is a more advanced application of the same strategy. The lemma states that a certain kind of coloring on
Parity_of_zero
travel, tourism, insurance
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travel, tourism, insurance