東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Simplicial methods for higher catego...

Paoli, Simona.

FindBook

Google Book

Amazon

博客來

Simplicial methods for higher categories = segal-type models of weak n-categories /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Simplicial methods for higher categories/ by Simona Paoli.
其他題名:	segal-type models of weak n-categories /
作者:	Paoli, Simona.
出版者:	Cham :Springer International Publishing : : 2019.,
面頁冊數:	xxii, 343 p. :ill., digital ;24 cm.
內容註:	Part I -- Higher Categories: Introduction and Background -- An Introduction to Higher Categories -- Multi-simplicial techniques -- An Introduction to the three Segal-type models -- Techniques from 2-category theory -- Part II -- The Three Segal-Type Models and Segalic Pseudo-Functors -- Homotopically discrete n-fold categories -- The Definition of the three Segal-type models -- Properties of the Segal-type models -- Pseudo-functors modelling higher structures -- Part III -- Rigidification of Weakly Globular Tamsamani n-Categories by Simpler Ones -- Rigidifying weakly globular Tamsamani n-categories -- Part IV. Weakly globular n-fold categories as a model of weak n-categories -- Functoriality of homotopically discrete objects -- Weakly Globular n-Fold Categories as a Model of Weak n-Categories -- Conclusions and further directions -- A Proof of Lemma 0.1.4 -- References -- Index.
Contained By:	Springer Nature eBook
標題:	Categories (Mathematics) -
電子資源:	https://doi.org/10.1007/978-3-030-05674-2
ISBN:	9783030056742

Simplicial methods for higher categories = segal-type models of weak n-categories /
Paoli, Simona.

Simplicial methods for higher categoriessegal-type models of weak n-categories /[electronic resource] :by Simona Paoli. - Cham :Springer International Publishing :2019. - xxii, 343 p. :ill., digital ;24 cm. - Algebra and applications,v.261572-5553 ;. - Algebra and applications ;v.26..

Part I -- Higher Categories: Introduction and Background -- An Introduction to Higher Categories -- Multi-simplicial techniques -- An Introduction to the three Segal-type models -- Techniques from 2-category theory -- Part II -- The Three Segal-Type Models and Segalic Pseudo-Functors -- Homotopically discrete n-fold categories -- The Definition of the three Segal-type models -- Properties of the Segal-type models -- Pseudo-functors modelling higher structures -- Part III -- Rigidification of Weakly Globular Tamsamani n-Categories by Simpler Ones -- Rigidifying weakly globular Tamsamani n-categories -- Part IV. Weakly globular n-fold categories as a model of weak n-categories -- Functoriality of homotopically discrete objects -- Weakly Globular n-Fold Categories as a Model of Weak n-Categories -- Conclusions and further directions -- A Proof of Lemma 0.1.4 -- References -- Index.

This monograph presents a new model of mathematical structures called weak $n$-categories. These structures find their motivation in a wide range of fields, from algebraic topology to mathematical physics, algebraic geometry and mathematical logic. While strict $n$-categories are easily defined in terms associative and unital composition operations they are of limited use in applications, which often call for weakened variants of these laws. The author proposes a new approach to this weakening, whose generality arises not from a weakening of such laws but from the very geometric structure of its cells; a geometry dubbed weak globularity. The new model, called weakly globular $n$-fold categories, is one of the simplest known algebraic structures yielding a model of weak $n$-categories. The central result is the equivalence of this model to one of the existing models, due to Tamsamani and further studied by Simpson. This theory has intended applications to homotopy theory, mathematical physics and to long-standing open questions in category theory. As the theory is described in elementary terms and the book is largely self-contained, it is accessible to beginning graduate students and to mathematicians from a wide range of disciplines well beyond higher category theory. The new model makes a transparent connection between higher category theory and homotopy theory, rendering it particularly suitable for category theorists and algebraic topologists. Although the results are complex, readers are guided with an intuitive explanation before each concept is introduced, and with diagrams showing the inter-connections between the main ideas and results.

ISBN: 9783030056742

Standard No.: 10.1007/978-3-030-05674-2doiSubjects--Topical Terms:

525955
Categories (Mathematics)

LC Class. No.: QA169 / .P36 2019

Dewey Class. No.: 511.3

Simplicial methods for higher categories = segal-type models of weak n-categories /
LDR:03656nmm a2200349 a 4500 001 2243230
003 DE-He213
005 20200629114219.0
006 m d
007 cr nn 008maaau
008 211207s2019 sz s 0 eng d
020 $a 9783030056742 $q (electronic bk.)
020 $a 9783030056735 $q (paper)
024 7 $a 10.1007/978-3-030-05674-2 $2 doi
035 $a 978-3-030-05674-2
040 $a GP $c GP
041 0 $a eng
050 4 $a QA169 $b .P36 2019
072 7 $a PBC $2 bicssc
072 7 $a MAT002010 $2 bisacsh
072 7 $a PBC $2 thema
072 7 $a PBF $2 thema
082 0 4 $a 511.3 $2 23
090 $a QA169 $b .P211 2019
100 1 $a Paoli, Simona. $3 3503174
245 1 0 $a Simplicial methods for higher categories $h [electronic resource] : $b segal-type models of weak n-categories / $c by Simona Paoli.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2019.
300 $a xxii, 343 p. : $b ill., digital ; $c 24 cm.
490 1 $a Algebra and applications, $x 1572-5553 ; $v v.26
505 0 $a Part I -- Higher Categories: Introduction and Background -- An Introduction to Higher Categories -- Multi-simplicial techniques -- An Introduction to the three Segal-type models -- Techniques from 2-category theory -- Part II -- The Three Segal-Type Models and Segalic Pseudo-Functors -- Homotopically discrete n-fold categories -- The Definition of the three Segal-type models -- Properties of the Segal-type models -- Pseudo-functors modelling higher structures -- Part III -- Rigidification of Weakly Globular Tamsamani n-Categories by Simpler Ones -- Rigidifying weakly globular Tamsamani n-categories -- Part IV. Weakly globular n-fold categories as a model of weak n-categories -- Functoriality of homotopically discrete objects -- Weakly Globular n-Fold Categories as a Model of Weak n-Categories -- Conclusions and further directions -- A Proof of Lemma 0.1.4 -- References -- Index.
520 $a This monograph presents a new model of mathematical structures called weak $n$-categories. These structures find their motivation in a wide range of fields, from algebraic topology to mathematical physics, algebraic geometry and mathematical logic. While strict $n$-categories are easily defined in terms associative and unital composition operations they are of limited use in applications, which often call for weakened variants of these laws. The author proposes a new approach to this weakening, whose generality arises not from a weakening of such laws but from the very geometric structure of its cells; a geometry dubbed weak globularity. The new model, called weakly globular $n$-fold categories, is one of the simplest known algebraic structures yielding a model of weak $n$-categories. The central result is the equivalence of this model to one of the existing models, due to Tamsamani and further studied by Simpson. This theory has intended applications to homotopy theory, mathematical physics and to long-standing open questions in category theory. As the theory is described in elementary terms and the book is largely self-contained, it is accessible to beginning graduate students and to mathematicians from a wide range of disciplines well beyond higher category theory. The new model makes a transparent connection between higher category theory and homotopy theory, rendering it particularly suitable for category theorists and algebraic topologists. Although the results are complex, readers are guided with an intuitive explanation before each concept is introduced, and with diagrams showing the inter-connections between the main ideas and results.
650 0 $a Categories (Mathematics) $3 525955
650 1 4 $a Category Theory, Homological Algebra. $3 899944
650 2 4 $a Algebraic Topology. $3 891269
650 2 4 $a Mathematical Physics. $3 1542352
650 2 4 $a Algebraic Geometry. $3 893861
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Algebra and applications ; $v v.26. $3 3503175
856 4 0 $u https://doi.org/10.1007/978-3-030-05674-2
950 $a Mathematics and Statistics (SpringerNature-11649)