Toposes are adhesive

Stephen Lack; Pawel Sobociński

doi:10.1007/11841883_14

Toposes are adhesive

Stephen Lack^*, Pawel Sobociński

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

35 Citations (Scopus)

Abstract

Adhesive categories have recently been proposed as a categorical foundation for facets of the theory of graph transformation, and have also been used to study techniques from process algebra for reasoning about concurrency. Here we continue our study of adhesive categories by showing that toposes are adhesive. The proof relies on exploiting the relationship between adhesive categories, Brown and Janelidze's work on generalised van Kampen theorems as well as Grothendieck's theory of descent.

Original language	English
Title of host publication	Graph Transformations
Subtitle of host publication	Third International Conference, ICGT 2006 Natal, Rio Grande do Norte, Brazil, September 17-23, 2006 Proceedings
Editors	Andrea Corradini, Ugo Montanari, Hartmut Ehrig, Leila Ribeiro
Place of Publication	Berlin; New York
Publisher	Springer, Springer Nature
Pages	184-198
Number of pages	15
ISBN (Electronic)	9783540388722
ISBN (Print)	3540388702, 9783540388708
DOIs	https://doi.org/10.1007/11841883_14
Publication status	Published - Sept 2006
Externally published	Yes
Event	3rd International Conference on Graph Transformations, ICGT - 2006 - Natal, Brazil Duration: 17 Sept 2006 → 23 Sept 2006

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4178 LNCS
ISSN (Print)	03029743
ISSN (Electronic)	16113349

Other

Other	3rd International Conference on Graph Transformations, ICGT - 2006
Country/Territory	Brazil
City	Natal
Period	17/09/06 → 23/09/06

Access to Document

10.1007/11841883_14

Cite this

Lack, S., & Sobociński, P. (2006). Toposes are adhesive. In A. Corradini, U. Montanari, H. Ehrig, & L. Ribeiro (Eds.), Graph Transformations: Third International Conference, ICGT 2006 Natal, Rio Grande do Norte, Brazil, September 17-23, 2006 Proceedings (pp. 184-198). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4178 LNCS). Springer, Springer Nature. https://doi.org/10.1007/11841883_14

Lack, Stephen ; Sobociński, Pawel. / Toposes are adhesive. Graph Transformations: Third International Conference, ICGT 2006 Natal, Rio Grande do Norte, Brazil, September 17-23, 2006 Proceedings. editor / Andrea Corradini ; Ugo Montanari ; Hartmut Ehrig ; Leila Ribeiro. Berlin; New York : Springer, Springer Nature, 2006. pp. 184-198 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Toposes are adhesive",

abstract = "Adhesive categories have recently been proposed as a categorical foundation for facets of the theory of graph transformation, and have also been used to study techniques from process algebra for reasoning about concurrency. Here we continue our study of adhesive categories by showing that toposes are adhesive. The proof relies on exploiting the relationship between adhesive categories, Brown and Janelidze's work on generalised van Kampen theorems as well as Grothendieck's theory of descent.",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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Lack, S & Sobociński, P 2006, Toposes are adhesive. in A Corradini, U Montanari, H Ehrig & L Ribeiro (eds), Graph Transformations: Third International Conference, ICGT 2006 Natal, Rio Grande do Norte, Brazil, September 17-23, 2006 Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4178 LNCS, Springer, Springer Nature, Berlin; New York, pp. 184-198, 3rd International Conference on Graph Transformations, ICGT - 2006, Natal, Brazil, 17/09/06. https://doi.org/10.1007/11841883_14

Toposes are adhesive. / Lack, Stephen; Sobociński, Pawel.
Graph Transformations: Third International Conference, ICGT 2006 Natal, Rio Grande do Norte, Brazil, September 17-23, 2006 Proceedings. ed. / Andrea Corradini; Ugo Montanari; Hartmut Ehrig; Leila Ribeiro. Berlin; New York: Springer, Springer Nature, 2006. p. 184-198 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4178 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

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AU - Lack, Stephen

AU - Sobociński, Pawel

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N2 - Adhesive categories have recently been proposed as a categorical foundation for facets of the theory of graph transformation, and have also been used to study techniques from process algebra for reasoning about concurrency. Here we continue our study of adhesive categories by showing that toposes are adhesive. The proof relies on exploiting the relationship between adhesive categories, Brown and Janelidze's work on generalised van Kampen theorems as well as Grothendieck's theory of descent.

AB - Adhesive categories have recently been proposed as a categorical foundation for facets of the theory of graph transformation, and have also been used to study techniques from process algebra for reasoning about concurrency. Here we continue our study of adhesive categories by showing that toposes are adhesive. The proof relies on exploiting the relationship between adhesive categories, Brown and Janelidze's work on generalised van Kampen theorems as well as Grothendieck's theory of descent.

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DO - 10.1007/11841883_14

M3 - Conference proceeding contribution

AN - SCOPUS:33750245070

SN - 3540388702

SN - 9783540388708

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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EP - 198

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A2 - Corradini, Andrea

A2 - Montanari, Ugo

A2 - Ehrig, Hartmut

A2 - Ribeiro, Leila

PB - Springer, Springer Nature

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T2 - 3rd International Conference on Graph Transformations, ICGT - 2006

Y2 - 17 September 2006 through 23 September 2006

ER -

Lack S, Sobociński P. Toposes are adhesive. In Corradini A, Montanari U, Ehrig H, Ribeiro L, editors, Graph Transformations: Third International Conference, ICGT 2006 Natal, Rio Grande do Norte, Brazil, September 17-23, 2006 Proceedings. Berlin; New York: Springer, Springer Nature. 2006. p. 184-198. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/11841883_14

Toposes are adhesive

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