Small set (category theory)

For other uses of the term, see Small set.

In category theory, a small set is one in a fixed universe of sets (as the word universe is used in mathematics in general). Thus, the category of small sets is the category of all sets one cares to consider. This is used when one does not wish to bother with set-theoretic concerns of what is and what is not considered a set, which concerns would arise if one tried to speak of the category of "all sets".

A small set is not to be confused with a small category, which is a category in which the collection of arrows (and therefore also the collection of objects) is a set.

In other choices of foundations, such as Grothendieck universes, there exist both sets that belong to the universe, called “small sets” and sets that do not, such as the universe itself, “large sets”. We gain an intermediate notion of moderate set: a subset of the universe, which may be small or large. Every small set is moderate, but not conversely.

Since in many cases the choice of foundations is irrelevant, it makes sense to always say “small set” for emphasis even if one has in mind a foundation where all sets are small.

Similarly, a small family is a family indexed by a small set; the axiom of replacement (if it applies in the foundation in question) then says that the image of the family is also small.

See also

References

  • S. Mac Lane, Ieke Moerdijk, Sheaves in geometry and logic: a first introduction to topos theory, ISBN 0-387-97710-4, ISBN 3-540-97710-4, the chapter on "Categorical preliminaries"
  • Small set at the nLab

Read other articles:

Distingsi

Artikel ini perlu diwikifikasi agar memenuhi standar kualitas Wikipedia. Anda dapat memberikan bantuan berupa penambahan pranala dalam, atau dengan merapikan tata letak dari artikel ini. Untuk keterangan lebih lanjut, klik [tampil] di bagian kanan. Mengganti markah HTML dengan markah wiki bila dimungkinkan. Tambahkan pranala wiki. Bila dirasa perlu, buatlah pautan ke artikel wiki lainnya dengan cara menambahkan [[ dan ]] pada kata yang bersangkutan (lihat WP:LINK untuk keterangan lebih lanjut...

 

Foreign Affairs

Foreign AffairsRedakturGideon RoseMantan editorJames F. Hoge, Jr.KategoriUrusan luar negeriFrekuensiDwibulananTotal sirkulasi(2013)163,134[1]Terbitan pertamaSeptember 1922 (September 1922)PerusahaanCouncil on Foreign RelationsNegaraAmerika SerikatBerpusat diNew York City, New YorkBahasaInggrisSitus webwww.foreignaffairs.com Foreign Affairs adalah jurnal hubungan internasional dan kebijakan luar negeri Amerika Serikat.[2] Jurnal ini diterbitkan enam kali setahun sejak 1922...

 

Nero (Devil May Cry)

Fictional character NeroDevil May Cry characterNero in Devil May Cry 5 (2019)First appearanceDevil May Cry 4 (2008)Created byBingo MorihashiDesigned byTatsuya YoshikawaVoiced byEN: Johnny Yong BoschJP: Kaito IshikawaMotion captureJohnny Yong BoschIn-universe informationSpeciesDevil-Human Hybrid Nero (Japanese: ネロ) is a character in Devil May Cry, an action-adventure hack and slash video game series by Japanese developer and publisher Capcom. He is the nephew of original Devil May Cry pro...

COVID-19 vaccination in Italy

Immunization plan against COVID-19 in Italy COVID-19 vaccination campaign in ItalyItaly is reborn with a flower – Vaccination against COVID-19Native name Vaccinazione anti COVID-19Date27 December 2020 (2020-12-27) – presentLocationItalyCauseCOVID-19 pandemicOrganised bySpecial commissioner of the GovernmentParticipants144,608,839[1] doses administered47,947,097[1] people are fully vaccinated as of 05 Apr 2024Outcome90+ % of the Italian population a...

 

Serse Coppi

Cet article est une ébauche concernant un coureur cycliste italien. Vous pouvez partager vos connaissances en l’améliorant (comment ?). Pour plus d’informations, voyez le projet cyclisme. Pour les articles homonymes, voir Coppi. Serse CoppiInformationsNaissance 19 mars 1923Castellania CoppiDécès 29 juin 1951 (à 28 ans)TurinNationalité italienneÉquipes professionnelles 1945-1948Bianchi1949-1950Bianchi-Ursus1951Bianchi-PirelliVue de la sépulture.modifier - modifier le cod...

 

Molo San Vincenzo Lighthouse

LighthouseMolo San Vincenzo Molo San Vincenzo LighthouseLocationNaplesCampaniaItalyCoordinates40°49′58″N 14°16′20″E / 40.832853°N 14.272133°E / 40.832853; 14.272133TowerConstructed1487(first)1495 (second)1843 (third)Foundationstone baseConstructionmasonry towerAutomatedyesHeight24 metres (79 ft)Shapecylindrical tower with balcony and lantern atop a concrete baseMarkingsred tower, white lantern, grey metallic lantern domePower sourcemains electricit...

14e cérémonie des Saturn Awards

14e cérémonie des Saturn Awards Saturn Awards Organisée par Academy of Science Fiction, Fantasy and Horror Films Détails Date 17 mai 1987 Lieu États-Unis Site web http://www.saturnawards.org/ Résumé Meilleur film de science-fiction Aliens, le retour Meilleur film fantastique La Tête dans les nuages Meilleur film d'horreur La Mouche Chronologie 13e cérémonie des Saturn Awards 15e cérémonie des Saturn Awards modifier  La 14e cérémonie des Saturn Awards, r...

 

Ricardo (footballer, born 1971)

Spanish footballer and manager In this Spanish name, the first or paternal surname is López and the second or maternal family name is Felipe. Ricardo Ricardo playing for Osasuna in 2008Personal informationFull name Ricardo López Felipe[1]Date of birth (1971-12-30) 30 December 1971 (age 52)[1]Place of birth Madrid, SpainHeight 1.87 m (6 ft 1+1⁄2 in)[1]Position(s) GoalkeeperYouth career Atlético MadridSenior career*Years Team Apps (Gl...

 

Neutral network (evolution)

Set of genes all related by point mutations that have equivalent function or fitness Not to be confused with Neural network or Network-neutral data center. A neutral network is a set of genes all related by point mutations that have equivalent function or fitness.[1] Each node represents a gene sequence and each line represents the mutation connecting two sequences. Neutral networks can be thought of as high, flat plateaus in a fitness landscape. During neutral evolution, genes can ra...

Decision theory

Branch of applied probability theory Part of a series onMathematics History Outline Index Areas Number theory Geometry Algebra Calculus and Analysis Discrete mathematics Logic and Set theory Probability Statistics and Decision theory Relationship with sciences Physics Chemistry Geosciences Computation Biology Linguistics Economics Philosophy Education Mathematics Portalvte The mythological judgement of Paris required selecting from three incomparable alternatives (the goddesses shown). Decisi...

 

2018 European Figure Skating Championships

Figure skating competition 2018 European Figure Skating ChampionshipsMegasport Arena during the first competitive dayType:ISU ChampionshipDate:15-21 January 2018Season:2017–18Location:Moscow, RussiaVenue:Megasport Sport PalaceChampionsMen's singles: Javier FernándezLadies' singles: Alina ZagitovaPairs: Evgenia Tarasova / Vladimir MorozovIce dance: Gabriella Papadakis / Guillaume CizeronNavigationPrevious: 2017 European ChampionshipsNext: 2019 European Championships The 2018 European Figure...

 

Indri

Untuk kegunaan lain, lihat Indri (disambiguasi). Indri Indri indri Rekaman Status konservasiTerancam kritisIUCN10826 TaksonomiKerajaanAnimaliaFilumChordataKelasMammaliaOrdoPrimatesFamiliIndriidaeGenusIndriSpesiesIndri indri (Gmelin, 1788) Tata namaSinonim taksonGenus: Indris Cuvier, 1800 Lichanotus Illiger, 1811 Indrium Rafinesque, 1815 Lichanotes Temminck, 1827 Pithelemur Lesson, 1840 Spesies: Lemur indri Gmelin, 1788 Indri brevicaudatus E. Geoffroy and G. Cuvier, 1796 Indri niger Lacépède...

Державний комітет телебачення і радіомовлення України

Державний комітет телебачення і радіомовлення України (Держкомтелерадіо) Приміщення комітетуЗагальна інформаціяКраїна  УкраїнаДата створення 2003Керівне відомство Кабінет Міністрів УкраїниРічний бюджет 1 964 898 500 ₴[1]Голова Олег НаливайкоПідвідомчі ор...

 

Federal Hall

Monumento Conmemorativo Federal Hall Monumento Conmemorativo Federal HallUbicación Monumento Conmemorativo Federal Hall Ubicación en Ciudad de Nueva YorkCoordenadas 40°42′26″N 74°00′37″O / 40.7072, -74.0103Dirección Wall and Nassau Sts.Ubicación Nueva York Nueva YorkCondado (s) Nueva YorkDatos generalesAgregado al NRHP 01966-10-15 15 de octubre de 1966Núm. de referencia 66000095[1]​[editar datos en Wikidata] Federal Hall está localizado en ...

 

Jonah Abutu

Nigerian footballer This article has multiple issues. Please help improve it or discuss these issues on the talk page. (Learn how and when to remove these template messages) This article is an orphan, as no other articles link to it. Please introduce links to this page from related articles; try the Find link tool for suggestions. (February 2022) This biography of a living person needs additional citations for verification. Please help by adding reliable sources. Contentious material about li...

لويس الثاني ملك فرنسا

لويس الثاني (بالفرنسية: Louis II le Bègue)‏  لويس الثاني بريشة لويس اميل 1837، قصر فرساي. ملك الفرنجة. مملكة الفرنجة الغربية فترة الحكم6 تشرين الأول 877 ـ 11 نيسان 879 نوع الحكم ملكي 8 كانون الأول 877 في مدينة كومبيين/ 7 أيلول 878 في مدينة تروا شارل الثاني الأصلع لويس الثالث (879 ـ 882) و كارلوم�...

 

معاداة الكوريين

مظاهرة في اليابان تصوّر معادة الكوريين معاداة الكوريين ((هانغل: 반한 감정)) ، هي مصطلح ينطبق على فئة من المجتمع المعارضة للوجود الكوري، والتي يشمل المجتمع الكوري وثقافتهم، بالإضافة إلى الأحداث السياسية كالإستعمار الياباني في شبه الجزيرة الكورية وقضية صخور ليانكورت.[1] ...

 

الإسكندر (فيلم)

الإسكندرAlexander (بالإنجليزية) ملصق الفيلم الترويجيمعلومات عامةالصنف الفني  القائمة ... فيلم دراما[1][2] — فيلم أكشن — فيلم سيرة ذاتية — فيلم حربي — فيلم متعلّق بالمثليين أو المتحولين الموضوع الإسكندر الأكبر تاريخ الصدور 24 ديسمبر 2004 (أمريكا)3 ديسمبر 2004 (اليونان)...

Spillover infection

Occurs when a reservoir population causes an epidemic in a novel host population Spillover infection, also known as pathogen spillover and spillover event, occurs when a reservoir population with a high pathogen prevalence comes into contact with a novel host population. The pathogen is transmitted from the reservoir population and may or may not be transmitted within the host population.[1] Due to climate change and land use expansion, the risk of viral spillover is predicted to sign...

 

Карачаевцы

Карачаевцы Современное самоназвание карач.-балк. къарачайлыла, таўлула, аланла [1] (чернореченцы, горцы, жители гор, аланы)[2] Алан, используется как обращение к соплеменнику. Численность и ареал Всего: ок. 300 000  Россия: 226 271 (2021)[3], 218 403 (2010)[4]  Карачаево-Че�...