"ক্যাটাগরি তত্ত্ব" পাতাটির দুইটি সংশোধিত সংস্করণের মধ্যে পার্থক্য

সম্পাদনা সারাংশ নেই
(নতুন পৃষ্ঠা: ===ক্যাটাগরি তত্ত্ব=== <math>a^2+b^2</math>)
 
 
===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>
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== 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==
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*{{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}}
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