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2-Fold Structures and Homotopy Theory = = 2 Katli Yapilar ve Homotopi Teorisi.

Record Type:	Electronic resources : Monograph/item
Title/Author:	2-Fold Structures and Homotopy Theory =/
Reminder of title:	2 Katli Yapilar ve Homotopi Teorisi.
remainder title:	2 Katli Yapilar ve Homotopi Teorisi.
Author:	Haderi, Redi.
Description:	1 online resource (144 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 84-11, Section: B.
Contained By:	Dissertations Abstracts International84-11B.
Subject:	Language. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30452949click for full text (PQDT)
ISBN:	9798379482510

2-Fold Structures and Homotopy Theory = = 2 Katli Yapilar ve Homotopi Teorisi.
Haderi, Redi.

2-Fold Structures and Homotopy Theory =2 Katli Yapilar ve Homotopi Teorisi.2 Katli Yapilar ve Homotopi Teorisi. - 1 online resource (144 pages)

Source: Dissertations Abstracts International, Volume: 84-11, Section: B.

Thesis (Ph.D.)--Bilkent Universitesi (Turkey), 2023.

Includes bibliographical references

It is well-known that correspondences between categories, also known as profunctors, serve in classifying functors. More precisely, every functor F : X → A straightens into a lax mapping XF : A → Catprof from A into a 2-category of categories and profunctors ([45]). We give a conceptual treatment of this fact from the lens of double category theory, contending the latter to be most natural environment to express this result.Then we venture into the world of simplicial sets and prove an analogous theorem. The notion of correspondence is easy to extend to simplicial sets, but a suitable double category may not be formed due to the lack of a natural tensor product. Nonetheless, we show that there is a natural simplicial category structure once we invoke higher correspondences. In proving our result we extend some notions from double category theory into the world of simplicial categories. As an application we obtain a realization of Lurie's prediction that inner fibrations are classified by mappings into a higher category of correspondences between ∞-categories.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798379482510Subjects--Topical Terms:

643551
Language.
Index Terms--Genre/Form:

542853
Electronic books.

2-Fold Structures and Homotopy Theory = = 2 Katli Yapilar ve Homotopi Teorisi.
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100 1 $a Haderi, Redi. $3 3698298
245 1 0 $a 2-Fold Structures and Homotopy Theory = $b 2 Katli Yapilar ve Homotopi Teorisi.
246 3 1 $a 2 Katli Yapilar ve Homotopi Teorisi.
264 0 $c 2023
300 $a 1 online resource (144 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
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500 $a Source: Dissertations Abstracts International, Volume: 84-11, Section: B.
500 $a Advisor: Unlu, Ozgun.
502 $a Thesis (Ph.D.)--Bilkent Universitesi (Turkey), 2023.
504 $a Includes bibliographical references
520 $a It is well-known that correspondences between categories, also known as profunctors, serve in classifying functors. More precisely, every functor F : X → A straightens into a lax mapping XF : A → Catprof from A into a 2-category of categories and profunctors ([45]). We give a conceptual treatment of this fact from the lens of double category theory, contending the latter to be most natural environment to express this result.Then we venture into the world of simplicial sets and prove an analogous theorem. The notion of correspondence is easy to extend to simplicial sets, but a suitable double category may not be formed due to the lack of a natural tensor product. Nonetheless, we show that there is a natural simplicial category structure once we invoke higher correspondences. In proving our result we extend some notions from double category theory into the world of simplicial categories. As an application we obtain a realization of Lurie's prediction that inner fibrations are classified by mappings into a higher category of correspondences between ∞-categories.
520 $a Profunktorler olarak da bilinen kategoriler arasindaki temci tekabullerin, funktorleri siniflandirmaya hizmet ettigi iyi bilinmektedir. Daha agik olarak ifade etimek gerekirse, her F : X → A funktoru, A kategorisinden kategoriler ve pro- funktorler 2-kategorisine giden gevsek bir XF : A → Catprof funktoru olarak duzlesir ((45)). Bu gercegi cifte kategori teorisinin merceginden ifade ediyoruz ve bu teorinin bu sonucu ifade etmek icin en dogal ortam oldugunu iddia ediyoruz.Daha sonra simpleksel kumeler dunyasina giriyoruz ve esdeger bir teo- remi kanitliyoruz. o Tekabuller kavramini simpleksel kumelere genisletmek ko- laydir, ancak uygun bir tensor carpiminin olmamasi nedeniyle cifte kategori olusturulamayabilir. Biz daha yuksek tekabuller kullanarak, en azindan, dogal bir simpleksel kategori yapisi oldugunu gosteriyoruz. Sonucumuzu kanitlarken, cifte kategori teorisindeki bazi kavramlari simpleksel kategoriler dunyasina genisletiyoruz. Bir uygulama olarak Lurie'nin ic lif demetlerinin, oc-kategoriler arasindaki daha yuksek tekabullere giden funetorler ile siniflandirildigina dair ongorusunu kanitliyoruz.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2023
538 $a Mode of access: World Wide Web
650 4 $a Language. $3 643551
650 4 $a Construction. $3 3561054
650 4 $a Algebra. $3 516203
650 4 $a Collage. $3 546856
650 4 $a Mathematics. $3 515831
655 7 $a Electronic books. $2 lcsh $3 542853
690 $a 0679
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 783688
710 2 $a Bilkent Universitesi (Turkey). $3 1919057
773 0 $t Dissertations Abstracts International $g 84-11B.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30452949 $z click for full text (PQDT)