ক্যাটাগরি তত্ত্ব: সংশোধিত সংস্করণের মধ্যে পার্থক্য

বিষয়বস্তু বিয়োগ হয়েছে বিষয়বস্তু যোগ হয়েছে

রৈখিক

১৭:১২, ৩০ ডিসেম্বর ২০১৪ তারিখে সংশোধিত সংস্করণ

ক্যাটাগরি তত্ত্ব^[১] is used to formalize mathematics and its concepts as a collection of objects and arrows (also called morphisms). Category theory can be used to formalize concepts of other high-level abstractions such as set theory, ring theory, and group theory. Several terms used in category theory, including the term "morphism", differ from their uses within mathematics itself. In category theory, a "morphism" obeys a set of conditions specific to category theory itself. Thus, care must be taken to understand the context in which statements are made.

$a^{2}+b^{2}$

নোট

↑ Awodey 2006

তথ্যসূত্র

Adámek, Jiří; Herrlich, Horst; Strecker, George E. (১৯৯০)। Abstract and concrete categories। John Wiley & Sons। আইএসবিএন 0-471-60922-6।
Awodey, Steve (২০০৬)। Category Theory। Oxford Logic Guides। 49। Oxford University Press। আইএসবিএন 978-0-19-151382-4।

আরোও পড়ুন

Jean-Pierre Marquis (২০০৮)। From a Geometrical Point of View: A Study of the History and Philosophy of Category Theory। Springer Science & Business Media। আইএসবিএন 978-1-4020-9384-5।

বহিঃসংযোগ

Theory and Application of Categories, an electronic journal of category theory, full text, free, since 1995.
nLab, a wiki project on mathematics, physics and philosophy with emphasis on the n-categorical point of view.
André Joyal, CatLab, a wiki project dedicated to the exposition of categorical mathematics.
Hillman, Chris, A Categorical Primer, টেমপ্লেট:Citeseerx , a formal introduction to category theory.
Adamek, J.; Herrlich, H.; Stecker, G.। "Abstract and Concrete Categories-The Joy of Cats" (PDF)।
Category Theory স্ট্যানফোর্ড এনসাইক্লোপিডিয়া অফ ফিলোসফি-র ভুক্তি, লিখেছেন Jean-Pierre Marquis with an extensive bibliography.
List of academic conferences on category theory
Baez, John (১৯৯৬)। "The Tale of n-categories"। — An informal introduction to higher order categories.
WildCats is a category theory package for Mathematica. Manipulation and visualization of objects, morphisms, categories, functors, natural transformations, universal properties.
ইউটিউবে The catsters চ্যানেল, a channel about category theory.
টেমপ্লেট:Planetmath reference
Video archive of recorded talks relevant to categories, logic and the foundations of physics.
Interactive Web page which generates examples of categorical constructions in the category of finite sets.

[1] Awodey 2006

[১]

@@ ১ নং লাইন: / ১ নং লাইন: @@
-===ক্যাটাগরি তত্ত্ব===
+[[File:Commutative diagram for morphism.svg|right|thumb|200px|A category with objects ''X'', ''Y'', ''Z'' and morphisms ''f'', ''g'', ''g'' ∘ ''f'', and three identity morphisms (not shown) 1<sub>''X''</sub>, 1<sub>''Y''</sub> and 1<sub>''Z''</sub>.]]
-     <math>a^2+b^2</math>
+'''ক্যাটাগরি তত্ত্ব'''<ref>{{harnvb|Awodey|2006}}</ref> is used to formalize [[mathematics]] and its concepts as a collection of ''objects'' and ''arrows'' (also called [[morphism]]s). Category theory can be used to formalize concepts of other high-level [[abstractions]] such as [[set theory]], [[ring theory]], and [[group theory]]. Several terms used in category theory, including the term "morphism", differ from their uses within mathematics itself. In category theory, a "morphism" obeys a set of conditions specific to category theory itself. Thus, care must be taken to understand the context in which statements are made.
+<math>a^2+b^2</math>
+<!--
+== See also ==
+{{Portal|Category theory}}
+* [[Group theory]]
+* [[Domain theory]]
+* [[Enriched category|Enriched category theory]]
+* [[Glossary of category theory]]
+* [[Higher category theory]]
+* [[Higher-dimensional algebra]]
+* [[List of publications in mathematics#Category theory|Important publications in category theory]]
+* [[Outline of category theory]]
+* [[Timeline of category theory and related mathematics]]
+-->
+==নোট==
+{{Reflist}}
+==তথ্যসূত্র==
+*{{cite book|title=Abstract and concrete categories|last1=Adámek |first1=Jiří |last2=Herrlich |first2=Horst |last3=Strecker |first3=George E.|publisher=John Wiley & Sons|year=1990|isbn=0-471-60922-6|url=http://katmat.math.uni-bremen.de/acc/acc.htm}}
+*{{cite book
+ |first=Steve |last=Awodey |authorlink=Steve Awodey
+ |title=Category Theory
+ |url=http://books.google.com/books?id=IK_sIDI2TCwC
+ |year=2006 |publisher=Oxford University Press |isbn=978-0-19-151382-4
+ |series=Oxford Logic Guides |volume=49 |ref=harv}}
+<!--*{{cite web|url=http://folli.loria.fr/cds/1999/library/pdf/barrwells.pdf|title=Category Theory Lecture Notes|year=1999|accessdate=11 December 2009-12-11|first1=Michael |last1=Barr |first2=Charles |last2=Wells}} Based on their book ''Category Theory for Computing Science'', [http://crm.umontreal.ca/pub/Ventes/desc/PM023.html  Centre de recherches mathématiques CRM], 1999.
+*{{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}}.
+*{{citation
+ | last1 = Barr | first1 = Michael | author1-link = Michael Barr (mathematician)
+ | last2 = Wells | first2 = Charles | author2-link = Charles Wells (mathematician)
+ | edition = revised
+ | 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 50-52
+ | last1 = Borceux
+ | first1 = Francis
+}}
+*{{cite book
+ | title = Introduction to the theory of categories and functors
+ | publisher = Wiley
+ | year = 1968
+ | last1 = Bucur
+ | first1 = Ion
+ | last2 = Deleanu
+ | first2 = Aristide
+}}
+*{{cite book|last=Freyd|first=Peter J.|title=Abelian Categories|publisher=Harper and Row|location=New York|year=1964|url=http://www.tac.mta.ca/tac/reprints/articles/3/tr3abs.html|authorlink=Peter J. Freyd}}
+*{{cite book |title=Categories, allegories |publisher=North Holland |year=1990 |series=North Holland Mathematical Library |volume=39 |last1=Freyd  |first1=Peter J.  |last2=Scedrov  |first2=Andre |url=http://books.google.com/books?id=fCSJRegkKdoC |isbn=978-0-08-088701-2}}
+*{{cite book |first=Robert |last=Goldblatt |title=Topoi: The Categorial Analysis of Logic |url=http://books.google.com/books?id=AwLc-12-7LMC |year=2006 |publisher=Dover Publications |isbn=978-0-486-45026-1 |volume=94 |series=Studies in logic and the foundations of mathematics |edition=Reprint, revised |origyear=1979}}
+*{{cite book |first=William S. |last=Hatcher |title=The logical foundations of mathematics |url=http://books.google.com/books?id=qNXuAAAAMAAJ |year=1982 |publisher=Pergamon Press |series=Foundations & philosophy of science & technology |chapter=Ch. 8 |edition=2nd}}
+*{{Citation| last1= Herrlich |first1= Horst |last2=Strecker |first2=George E. |year=2007|edition=3rd|title=Category Theory |publisher= Heldermann Verlag Berlin  |isbn=978-3-88538-001-6}}.
+*{{cite book |first1=Masaki |last1=Kashiwara |first2=Pierre |last2=Schapira |title=Categories and Sheaves |url=http://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 |first2=Robert |last2=Rosebrugh |title=Sets for Mathematics |url=http://books.google.com/books?id=h3_7aZz9ZMoC |year=2003 |publisher=Cambridge University Press |isbn=978-0-521-01060-3}}
+*{{cite book |first1=F. W. |last1=Lawvere |first2=Stephen Hoel |last2=Schanuel |title=Conceptual Mathematics: A First Introduction to Categories |url=http://books.google.com/books?id=h0zOGPlFmcQC |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 |publisher=Cambridge University Press |year=2004  |isbn=978-0-521-53215-0 |series=London Math. Society Lecture Note Series |volume=298 |url=http://www.maths.gla.ac.uk/~tl/book.html}}
+*{{cite book|last=Lurie|first=Jacob|title=Higher topos theory|publisher=Princeton University Press|year=2009|series=Annals of Mathematics Studies |volume=170|arxiv=math.CT/0608040}}
+*{{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 5 |authorlink=Saunders Mac Lane |isbn=0-387-98403-8 |ref=harv}}
+*{{cite book |title=Algebra |last1=Mac Lane |first1=Saunders |first2=Garrett |last2=Birkhoff |publisher=Chelsea |year=1999| edition=2nd |isbn=0-8218-1646-2 |origyear=1967}}
+*{{cite journal|year=1996|title=Elements of basic category theory|journal=Technical Report|publisher=Technical University Berlin|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|title=A Concise Course in Algebraic Topology|publisher=University of Chicago Press|year=1999|isbn=0-226-51183-9}}
+*{{cite book |first=Mazzola |last=Guerino |title=The Topos of Music, Geometric Logic of Concepts, Theory, and Performance |publisher=Birkhäuser |location= |year=2002 |isbn=3-7643-5731-2 }}
+* {{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 | location=Cambridge | publisher=[[Cambridge University Press]] | year=2004 | isbn=0-521-83414-7 }}
+*{{cite book |first=Benjamin C. |last=Pierce |title=Basic Category Theory for Computer Scientists |url=http://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. |format=PDF}} Notes for a course offered as part of the MSc. in [[Mathematical Logic]], [[Manchester University]].
+*{{cite book|title=Homotopy theory of higher categories|last=Simpson|first=Carlos|arxiv=1001.4071}}, draft of a book.
+*{{cite book |first=Paul |last=Taylor |title=Practical Foundations of Mathematics |url=http://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}}.
+-->
+==আরোও পড়ুন==
+* {{cite book|author=Jean-Pierre Marquis|title=From a Geometrical Point of View: A Study of the History and Philosophy of Category Theory|year=2008|publisher=Springer Science & Business Media|isbn=978-1-4020-9384-5}}
+== বহিঃসংযোগ ==
+* [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], a wiki project on mathematics, physics and philosophy with emphasis on the ''n''-categorical point of view.
+* [[André Joyal]], [http://ncatlab.org/nlab CatLab], a wiki project dedicated to the exposition of categorical mathematics.
+* {{citation |first=Chris |last=Hillman |title=A Categorical Primer |id={{citeseerx|10.1.1.24.3264}}}}, a formal introduction to category theory.
+* {{cite web |first1=J. |last1=Adamek |first2=H. |last2=Herrlich |first3=G. |last3=Stecker  |title=Abstract and Concrete Categories-The Joy of Cats |format=PDF |url=http://katmat.math.uni-bremen.de/acc/acc.pdf}}
+* {{sep entry|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 |work= |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 reference|id=5622|title=Category Theory}}
+* [http://categorieslogicphysics.wikidot.com/events Video archive] of recorded talks relevant to categories, logic and the foundations of physics.
+* [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.
+{{DEFAULTSORT:Category Theory}}