國立虎尾科技大學 |

Simplicial Methods for Higher Categories = Segal-type Models of Weak n-Categories /

紀錄類型:	書目-語言資料,印刷品 : 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.
面頁冊數:	XXII, 343 p. 262 illus., 12 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Category theory (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. - 1st ed. 2019. - XXII, 343 p. 262 illus., 12 illus. in color.online resource. - Algebra and Applications,261572-5553 ;. - Algebra and Applications,20.

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:

1255325
Category theory (Mathematics).

LC Class. No.: QA169

Dewey Class. No.: 512.6

Simplicial Methods for Higher Categories = Segal-type Models of Weak n-Categories /
LDR:03987nam a22004095i 4500 001 1015397
003 DE-He213
005 20200629114219.0
007 cr nn 008mamaa
008 210106s2019 gw | s |||| 0|eng d
020 $a 9783030056742 $9 978-3-030-05674-2
024 7 $a 10.1007/978-3-030-05674-2 $2 doi
035 $a 978-3-030-05674-2
050 4 $a QA169
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 512.6 $2 23
100 1 $a Paoli, Simona. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1309522
245 1 0 $a Simplicial Methods for Higher Categories $h [electronic resource] : $b Segal-type Models of Weak n-Categories / $c by Simona Paoli.
250 $a 1st ed. 2019.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2019.
300 $a XXII, 343 p. 262 illus., 12 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Algebra and Applications, $x 1572-5553 ; $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 Category theory (Mathematics). $3 1255325
650 0 $a Homological algebra. $3 1255326
650 0 $a Algebraic topology. $3 678206
650 0 $a Mathematical physics. $3 527831
650 0 $a Algebraic geometry. $3 1255324
650 1 4 $a Category Theory, Homological Algebra. $3 678397
650 2 4 $a Algebraic Topology. $3 672209
650 2 4 $a Mathematical Physics. $3 786661
650 2 4 $a Algebraic Geometry. $3 670184
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030056735
776 0 8 $i Printed edition: $z 9783030056759
830 0 $a Algebra and Applications, $x 1572-5553 ; $v 20 $3 1261460
856 4 0 $u https://doi.org/10.1007/978-3-030-05674-2
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)