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Hardie, K. A.; Kamps, Klaus; Kieboom, R. W.

doi:10.1023/a:1011270417127

Cited by 21 publications

(15 citation statements)

References 33 publications

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“…The composition of paths is not associative: associativity is verified for equivalence classes of homotopies [38]. Thus, the bicategory COLOR and the bicategory TIMBRE can be considered as bigroupoids [39,40], that is, bicategories whose morphisms are weakly invertible (up to iso). A bigroupoid is a "bicategory [...] such that the 2-cells are strictly invertible and the 1-cells are invertible up to coherent isomorphism" [39], p. 313.…”

Section: Categorical Depictions Of Color and Timbre Gesturesmentioning

confidence: 99%

Color and Timbre Gestures: An Approach with Bicategories and Bigroupoids

Mannone

Santini²,

Adedoyin

et al. 2022

Mathematics

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White light can be decomposed into different colors, and a complex sound wave can be decomposed into its partials. While the physics behind transverse and longitudinal waves is quite different and several theories have been developed to investigate the complexity of colors and timbres, we can try to model their structural similarities through the language of categories. Then, we consider color mixing and color transition in painting, comparing them with timbre superposition and timbre morphing in orchestration and computer music in light of bicategories and bigroupoids. Colors and timbres can be a probe to investigate some relevant aspects of visual and auditory perception jointly with their connections. Thus, the use of categories proposed here aims to investigate color/timbre perception, influencing the computer science developments in this area.

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Section: Categorical Depictions Of Color and Timbre Gesturesmentioning

confidence: 99%

Color and Timbre Gestures: An Approach with Bicategories and Bigroupoids

Mannone

Santini²,

Adedoyin

et al. 2022

Mathematics

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“…Any algebraic model for (pointed) homotopy 2-types has an underlying 2-track groupoid. Using the globular description in Remark 3.1, the most direct comparison is to the bigroupoids of [12]. A pointed bigroupoid (resp.…”

Section: A2 Comparison To Bigroupoidsmentioning

confidence: 99%

“…BiGpd 2 (X ) denote the homotopy bigroupoid of a space X constructed in [12], where it was denoted 2 (X ).…”

Section: Proposition A5 Letmentioning

confidence: 99%

“…There are various algebraic models for homotopy 2-types in the literature, using 2-dimensional categorical structures. Let us mention the weak 2-groupoids of [15], the bigroupoids of [12], the double groupoids of [10], the two-typical double groupoids of [7], and the double groupoids with filling condition of [11].…”

Section: Appendix A: Models For Homotopy 2-typesmentioning

confidence: 99%

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2-track algebras and the Adams spectral sequence

Baues

Frankland

2016

J. Homotopy Relat. Struct.

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In previous work of the first author and Jibladze, the E 3 -term of the Adams spectral sequence was described as a secondary derived functor, defined via secondary chain complexes in a groupoid-enriched category. This led to computations of the E 3term using the algebra of secondary cohomology operations. In work with Blanc, an analogous description was provided for all higher terms E r . In this paper, we introduce 2-track algebras and tertiary chain complexes, and we show that the E 4 -term of the Adams spectral sequence is a tertiary Ext group in this sense. This extends the work with Jibladze, while specializing the work with Blanc in a way that should be more amenable to computations.

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“…Remark 5.13 The fundamental bigroupoid … 2 .X / of a space X was independently described by Hardie, Kamps and Kieboom in [26] and by Stevenson in [42]. The objects of … 2 .X / are the points x 2 X , the 1-cells f W x !…”

Section: Bicategorical Groups and Homotopy 3-typesmentioning

confidence: 99%

Comparing geometric realizations of tricategories

Cegarra¹,

Heredia²

2014

Algebr. Geom. Topol.

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This paper contains some contributions to the study of classifying spaces for tricategories, with applications to the homotopy theory of monoidal categories, bicategories, braided monoidal categories and monoidal bicategories. Any small tricategory has various associated simplicial or pseudosimplicial objects and we explore the relationship between three of them: the pseudosimplicial bicategory (so-called Grothendieck nerve) of the tricategory, the simplicial bicategory termed its Segal nerve and the simplicial set called its Street geometric nerve. We prove that the geometric realizations of all of these 'nerves of the tricategory' are homotopy equivalent. By using Grothendieck nerves we state the precise form in which the process of taking classifying spaces transports tricategorical coherence to homotopy coherence. Segal nerves allow us to prove that, under natural requirements, the classifying space of a monoidal bicategory is, in a precise way, a loop space. With the use of geometric nerves, we obtain simplicial sets whose simplices have a pleasing geometrical description in terms of the cells of the tricategory and we prove that, via the classifying space construction, bicategorical groups are a convenient algebraic model for connected homotopy 3-types.

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Cited by 21 publications

References 33 publications

Color and Timbre Gestures: An Approach with Bicategories and Bigroupoids

Color and Timbre Gestures: An Approach with Bicategories and Bigroupoids

2-track algebras and the Adams spectral sequence

Comparing geometric realizations of tricategories

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