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Baris 1: [[Berkas:Commutative diagram for morphism.svg\|ka\|jmpl\|200px\|Teori kategori. Sebuah kategori dengan objek ''X'', ''Y'', ''Z'', dan morfisme ''f'', ''g'', ''g'' ∘ ''f'', dan tiga morfisma identitas (tidak ditunjukkan) 1<sub>''X''</sub>, 1<sub>''Y''</sub>, dan 1<sub>''Z''</sub>.]] '''Teori kategori''' berhubungan dengan struktur [[matematika]] dan hubungan antar struktur tersebut secara abstrak. Saat ini kategori digunakan dalam matematika, informatika teori, dan [[fisika matematis]]. Kategori diperkenalkan pertama kali oleh [[Samuel Eilenberg]] dan [[Saunders Mac Lane]] pada tahun [[1942]]-[[1945]], dalam hubungannya dengan ~~topologi~~ [[topologi aljabar]]. == Definisi Kategori == Baris 51: == Konstruksi Kategori Baru dari Kategori yang Ada == ~~===Kategori Dual===~~ Sebarang kategori <math>\mathcal{C}</math> dapat dikonstruksi menjadi kategori baru dengan membalik setiap morfismanya tanpa mengubah objeknya. Kategori yang demikian disebut kategori ''dual'' dan dinotasikan sebagai <math>\mathcal{C}</math><sup>op</sup> == Lihat pula == {{Portal\|Matematika}} {{cols\|colwidth=26em}} * [[Teori domain]] * [[Kategori yang diperkaya\|Teori kategori yang diperkaya]] * [[Glosarium teori kategori]] * [[Teori grup]] * [[Teori kategori yang lebih tinggi]] * [[Aljabar berdimensi lebih tinggi]] * [[Daftar publikasi dalam matematika#Teori kategori\|Publikasi penting dalam teori kategori]] * [[Kalkulus Lambda]] * [[Garis besar teori kategori]] * [[Garis waktu teori kategori dan matematika terkait]] {{colend}} == Referensi == === Kutipan === {{Reflist}} === Sumber === * {{cite book \|title = Abstract and Concrete Categories \|last1 = Adámek \|first1 = Jiří \|last2 = Herrlich \|first2 = Horst \|author2-link = Horst Herrlich \|last3 = Strecker \|first3 = George E. \|publisher = Heldermann Verlag Berlin \|year = 2004 \|url = http://katmat.math.uni-bremen.de/acc/acc.htm \|access-date = 2020-11-26 \|archive-date = 2021-02-24 \|archive-url = https://web.archive.org/web/20210224031815/http://katmat.math.uni-bremen.de/acc/acc.htm \|dead-url = yes }} * {{citation \| last1 = Barr \| first1 = Michael \| author1-link = Michael Barr (mathematician) \| last2 = Wells \| first2 = Charles \| author2-link = Charles Wells (mathematician) \| edition = 3rd \| series = Reprints in Theory and Applications of Categories \| title = Category Theory for Computing Science \| url = http://www.tac.mta.ca/tac/reprints/articles/22/tr22abs.html \| volume = 22 \| year = 2012 \|origyear=1995 }}. * {{citation \| last1 = Barr \| first1 = Michael \| author1-link = Michael Barr (mathematician) \| last2 = Wells \| first2 = Charles \| author2-link = Charles Wells (mathematician) \| series = Reprints in Theory and Applications of Categories \| mr = 2178101 \| title = Toposes, Triples and Theories \| url = http://www.tac.mta.ca/tac/reprints/articles/12/tr12abs.html \| volume = 12 \| year = 2005 }}. * {{cite book \| title = Handbook of categorical algebra \| publisher = Cambridge University Press \| year = 1994 \| series = Encyclopedia of Mathematics and its Applications \|pages=50–52 \| last1 = Borceux \| first1 = Francis \| url = https://books.google.com/books?id=YfzImoopB-IC&q=%22Handbook+of+categorical+algebra%22&pg=PP1 \| isbn = 9780521441780 }} * {{cite book \|last=Freyd \|first=Peter J. \|title = Abelian Categories \|origyear=1964 \|url = http://www.tac.mta.ca/tac/reprints/articles/3/tr3abs.html \|authorlink=Peter J. Freyd \|year=2003 \|series=Reprints in Theory and Applications of Categories \|volume=3}} * {{cite book \|title = Categories, allegories \|publisher=North Holland \|year=1990 \|series=North Holland Mathematical Library \|volume=39 \|last1=Freyd \|first1=Peter J. \|author1-link=Peter J. Freyd \|last2=Scedrov \|first2=Andre \|url = https://books.google.com/books?id=fCSJRegkKdoC \|isbn = 978-0-08-088701-2 }} * {{cite book \|first=Robert \|last=Goldblatt \|authorlink=Robert Goldblatt \|title = Topoi: The Categorial Analysis of Logic \|url = https://books.google.com/books?id=AwLc-12-7LMC \|year=2006 \|publisher=Dover \|isbn = 978-0-486-45026-1 \|volume=94 \|series=Studies in logic and the foundations of mathematics \|origyear = 1979 }} * {{cite book \|last1= Herrlich \|first1= Horst \|author1-link=Horst Herrlich \|last2=Strecker \|first2=George E. \|year=2007 \|edition=3rd \|title = Category Theory \|url= https://archive.org/details/categorytheoryin0000herr \|publisher = Heldermann Verlag Berlin \|isbn = 978-3-88538-001-6}}. * {{cite book \|first1=Masaki \|last1=Kashiwara \|author1-link=Masaki Kashiwara \|first2=Pierre \|last2=Schapira \|author2-link=Pierre Schapira (mathematician) \|title = Categories and Sheaves \|url = https://books.google.com/books?id=K-SjOw_2gXwC \|year=2006 \|publisher=Springer \|isbn = 978-3-540-27949-5 \|volume=332 \|series=Grundlehren der Mathematischen Wissenschaften }} * {{cite book \|first1=F. William \|last1=Lawvere \|author1-link=William Lawvere \|first2=Robert \|last2=Rosebrugh \|title = Sets for Mathematics \|url = https://archive.org/details/setsformathemati0000lawv \|url-access=registration \|year=2003 \|publisher=Cambridge University Press \|isbn = 978-0-521-01060-3 }} * {{cite book \|first1=F. William \|last1=Lawvere \|first2=Stephen Hoel \|last2=Schanuel \|author2-link=Stephen Schanuel \|title = Conceptual Mathematics: A First Introduction to Categories \|url = https://archive.org/details/conceptualmathem00lawv \|url-access=registration \|year=2009 \|publisher=Cambridge University Press \|isbn = 978-0-521-89485-2 \|edition=2nd \|origyear=1997 }} * {{cite book \|last=Leinster \|first=Tom \|title=Higher Operads, Higher Categories \|journal=Higher Operads \|publisher=Cambridge University Press \|year=2004 \|isbn=978-0-521-53215-0 \|series=London Math. Society Lecture Note Series \|volume=298 \|pages=448 \|url=http://www.maths.gla.ac.uk/~tl/book.html \|bibcode=2004hohc.book.....L \|access-date=2006-04-03 \|archive-url=https://web.archive.org/web/20031025120434/http://www.maths.gla.ac.uk/~tl/book.html \|archive-date=2003-10-25 \|url-status=dead }} * {{cite book \|last=Leinster \|first=Tom \|title = Basic Category Theory \|publisher=Cambridge University Press \|year=2014 \|arxiv=1612.09375 \|url=https://books.google.com/books?id=Q3vsAwAAQBAJ \|isbn=9781107044241 \|volume=143 \|series=Cambridge Studies in Advanced Mathematics}} * {{cite book \|last=Lurie \|first=Jacob \|authorlink=Jacob Lurie \|title = Higher Topos Theory\| publisher=Princeton University Press \|year=2009 \|series=Annals of Mathematics Studies \|volume=170 \|arxiv=math.CT/0608040 \|mr=2522659 \|isbn=978-0-691-14049-0 }} * {{cite book \|last=Mac Lane \|first=Saunders \|title=Categories for the Working Mathematician \|publisher=Springer-Verlag \|year=1998 \|edition=2nd \|series=Graduate Texts in Mathematics \| volume=5 \|authorlink=Saunders Mac Lane \|isbn=978-0-387-98403-2 \|ref=harv \| mr=1712872\|title-link=Categories for the Working Mathematician }} * {{cite book \|title=Algebra \|last1=Mac Lane \|first1=Saunders \|author1-link=Saunders Mac Lane \|first2=Garrett \|last2=Birkhoff \|author2link=Garrett Birkhoff \|publisher=Chelsea \|year=1999\| edition=2nd \|isbn = 978-0-8218-1646-2 \|origyear=1967 }} * {{cite journal \|year=1996\|title=Elements of basic category theory \|journal=Technical Report\|volume=96 \|issue=5 \|url = http://citeseer.ist.psu.edu/martini96element.html \|first1=A. \|last1=Martini \|first2=H. \|last2=Ehrig \|first3=D. \|last3=Nunes}} * {{cite book \|last=May \|first=Peter \|authorlink=J. Peter May \|title=A Concise Course in Algebraic Topology\|publisher=University of Chicago Press\|year=1999 \|isbn=978-0-226-51183-2}} * {{cite book \|first=Guerino \|last=Mazzola \|authorlink=Guerino Mazzola \|title=The Topos of Music, Geometric Logic of Concepts, Theory, and Performance \|url=https://archive.org/details/toposofmusicgeom0000mazz \|publisher=Birkhäuser \|location= \|year=2002 \|isbn = 978-3-7643-5731-3 }} * {{cite book \|zbl=1034.18001 \|editor1-last=Pedicchio \|editor1-first = Maria Cristina \|editor2-last = Tholen \|editor2-first=Walter \|title = Categorical foundations. Special topics in order, topology, algebra, and sheaf theory \|series=Encyclopedia of Mathematics and Its Applications \|volume=97 \|publisher=[[Cambridge University Press]] \|year=2004 \|isbn = 978-0-521-83414-8 }} * {{cite book \|first=Benjamin C. \|last=Pierce \|authorlink=Benjamin C. Pierce \|title = Basic Category Theory for Computer Scientists \|url = https://books.google.com/books?id=ezdeaHfpYPwC \|year=1991 \|publisher=MIT Press \|isbn = 978-0-262-66071-6 }} * {{cite book \|title=An introduction to Category Theory in four easy movements \|year=2005 \|url=http://www.cs.man.ac.uk/~hsimmons/BOOKS/CatTheory.pdf \|last1=Schalk \|first1=A. \|last2=Simmons \|first2=H. \|access-date=2007-12-03 \|archive-url=https://web.archive.org/web/20170321152109/http://www.cs.man.ac.uk/~hsimmons/BOOKS/CatTheory.pdf \|archive-date=2017-03-21 \|url-status=dead }} Notes for a course offered as part of the MSc. in [[Mathematical Logic]], [[Manchester University]]. * {{cite book \|title = Homotopy theory of higher categories \|url = https://archive.org/details/arxiv-1001.4071 \|last=Simpson \|first=Carlos \|authorlink=Carlos Simpson \|arxiv=1001.4071 \|bibcode=2010arXiv1001.4071S \|year=2010 }}, draft of a book. * {{cite book \|first=Paul \|last=Taylor \|title=Practical Foundations of Mathematics \|url= https://books.google.com/books?id=iSCqyNgzamcC \|year=1999 \|publisher= Cambridge University Press \|isbn = 978-0-521-63107-5 \|series = Cambridge Studies in Advanced Mathematics \|volume = 59 }} * {{cite web \|url = http://www.dcs.ed.ac.uk/home/dt/CT/categories.pdf \|title = Category Theory Lecture Notes \|last=Turi \|first=Daniele \|date = 1996–2001 \|accessdate = 11 December 2009 }} Based on {{harvnb\|Mac Lane\|1998}}. == Bacaan lebih lanjut == * {{cite book \|first=Jean-Pierre \|last=Marquis \|title=From a Geometrical Point of View: A Study of the History and Philosophy of Category Theory \|year=2008 \|publisher=Springer \|isbn=978-1-4020-9384-5}} == Pranala luar == {{Commons category}} {{wikiquote}} * [http://www.tac.mta.ca/tac/ Theory and Application of Categories], an electronic journal of category theory, full text, free, since 1995. * [http://ncatlab.org/nlab nLab], sebuah proyek wiki tentang matematika, fisika dan filsafat dengan penekanan pada sudut pandang '' n '' - kategorikal. * [https://golem.ph.utexas.edu/category/ The n-Category Café], pada dasarnya sebuah kolokium tentang topik-topik dalam teori kategori. * [http://www.logicmatters.net/categories/ Category Theory], halaman web yang berisi tautan ke catatan kuliah dan buku-buku tentang teori kategori yang tersedia secara gratis. * {{citation \|first=Chris \|last=Hillman \|title=A Categorical Primer \|citeseerx=10.1.1.24.3264}}, pengantar formal untuk teori kategori. * {{cite web \|first1=J. \|last1=Adamek \|first2=H. \|last2=Herrlich \|first3=G. \|last3=Stecker \|title=Abstract and Concrete Categories-The Joy of Cats \|url=http://katmat.math.uni-bremen.de/acc/acc.pdf \|access-date=2020-11-26 \|archive-date=2015-04-21 \|archive-url=https://web.archive.org/web/20150421081851/http://katmat.math.uni-bremen.de/acc/acc.pdf \|dead-url=yes }} * {{SEP\|category-theory\|Category Theory\|Jean-Pierre Marquis}}, with an extensive bibliography. * [http://www.mta.ca/~cat-dist/ List of academic conferences on category theory] * {{cite web \|last=Baez \|first=John \|title=The Tale of ''n''-categories \|year=1996 \|website= \|publisher= \|url=http://math.ucr.edu/home/baez/week73.html}}—An informal introduction to higher order categories. * [http://wildcatsformma.wordpress.com WildCats] is a category theory package for [[Mathematica]]. Manipulation and visualization of objects, [[morphism]]s, categories, [[functor]]s, [[natural transformation]]s, [[universal properties]]. * {{YouTube\|user=TheCatsters\|title=The catsters}}, a channel about category theory. * {{PlanetMath\|urlname=9categorytheory\|title=Category theory}}. * [http://categorieslogicphysics.wikidot.com/events Video archive] of recorded talks relevant to categories, logic and the foundations of physics. * [https://web.archive.org/web/20080916162345/http://www.j-paine.org/cgi-bin/webcats/webcats.php Interactive Web page] which generates examples of categorical constructions in the category of finite sets. * [https://web.archive.org/web/20150109111227/http://category-theory.mitpress.mit.edu/index.html Category Theory for the Sciences], an instruction on category theory as a tool throughout the sciences. * [https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/ Category Theory for Programmers] A book in blog form explaining category theory for computer programmers. * [http://math.mit.edu/~dspivak/teaching/sp18/7Sketches.pdf Introduction to category theory.] {{Bidang matematika}} {{Teori kategori}} {{Ilmu Komputer}} {{Authority control}} {{DEFAULTSORT:Category Theory}} [[Kategori:Teori kategori\| ]] [[Kategori:Teori kategori yang lebih tinggi]] [[Kategori:Matematika]]