Limits and colimits in a category of lenses

Emma Chollet; Bryce Clarke; Michael Johnson; Maurine Songa; Vincent Wang; Gioele Zardini

Limits and colimits in a category of lenses

Emma Chollet, Bryce Clarke, Michael Johnson, Maurine Songa, Vincent Wang, Gioele Zardini

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

2 Citations (Scopus)

41 Downloads (Pure)

Abstract

Lenses are an important tool in applied category theory. While individual lenses have been widely used in applications, many of the mathematical properties of the corresponding categories of lenses have remained unknown. In this paper, we study the category of small categories and asymmetric delta lenses, and prove that it has several good exactness properties. These properties include the existence of certain limits and colimits, as well as so-called imported limits, such as imported products and imported pullbacks, which have arisen previously in applications. The category is also shown to be extensive, and it has an image factorisation system.

Original language	English
Title of host publication	Proceedings of the Fourth International Conference on Applied Category Theory
Editors	Kohei Kishida
Place of Publication	Cambridge, UK
Publisher	Open Publishing Association
Pages	164-177
Number of pages	14
Publication status	Published - 3 Nov 2022
Event	4th International Conference on Applied Category Theory, ACT 2021 - Cambridge, United Kingdom Duration: 12 Jul 2022 → 16 Jul 2022

Publication series

Name	Electronic Proceedings in Theoretical Computer Science, EPTCS
Publisher	Open Publishing Association
Volume	372
ISSN (Print)	2075-2180

Conference

Conference	4th International Conference on Applied Category Theory, ACT 2021
Country/Territory	United Kingdom
City	Cambridge
Period	12/07/22 → 16/07/22

Bibliographical note

Copyright © Chollet, Clarke, Johnson, Songa, Wang, Zardini. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

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Publisher version (open access)Final published version, 214 KBLicence: CC BY

https://cgi.cse.unsw.edu.au/~eptcs/paper.cgi?ACT2021.12Licence: CC BY

Cite this

Chollet, E., Clarke, B., Johnson, M., Songa, M., Wang, V., & Zardini, G. (2022). Limits and colimits in a category of lenses. In K. Kishida (Ed.), Proceedings of the Fourth International Conference on Applied Category Theory (pp. 164-177). (Electronic Proceedings in Theoretical Computer Science, EPTCS; Vol. 372). Open Publishing Association. https://cgi.cse.unsw.edu.au/~eptcs/paper.cgi?ACT2021.12

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title = "Limits and colimits in a category of lenses",

abstract = "Lenses are an important tool in applied category theory. While individual lenses have been widely used in applications, many of the mathematical properties of the corresponding categories of lenses have remained unknown. In this paper, we study the category of small categories and asymmetric delta lenses, and prove that it has several good exactness properties. These properties include the existence of certain limits and colimits, as well as so-called imported limits, such as imported products and imported pullbacks, which have arisen previously in applications. The category is also shown to be extensive, and it has an image factorisation system.",

author = "Emma Chollet and Bryce Clarke and Michael Johnson and Maurine Songa and Vincent Wang and Gioele Zardini",

note = "Copyright {\textcopyright} Chollet, Clarke, Johnson, Songa, Wang, Zardini. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.; 4th International Conference on Applied Category Theory, ACT 2021 ; Conference date: 12-07-2022 Through 16-07-2022",

year = "2022",

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language = "English",

series = "Electronic Proceedings in Theoretical Computer Science, EPTCS",

publisher = "Open Publishing Association",

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Chollet, E, Clarke, B, Johnson, M, Songa, M, Wang, V & Zardini, G 2022, Limits and colimits in a category of lenses. in K Kishida (ed.), Proceedings of the Fourth International Conference on Applied Category Theory. Electronic Proceedings in Theoretical Computer Science, EPTCS, vol. 372, Open Publishing Association, Cambridge, UK, pp. 164-177, 4th International Conference on Applied Category Theory, ACT 2021, Cambridge, United Kingdom, 12/07/22. <https://cgi.cse.unsw.edu.au/~eptcs/paper.cgi?ACT2021.12>

Limits and colimits in a category of lenses. / Chollet, Emma; Clarke, Bryce; Johnson, Michael et al.
Proceedings of the Fourth International Conference on Applied Category Theory. ed. / Kohei Kishida. Cambridge, UK: Open Publishing Association, 2022. p. 164-177 (Electronic Proceedings in Theoretical Computer Science, EPTCS; Vol. 372).

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

TY - GEN

T1 - Limits and colimits in a category of lenses

AU - Chollet, Emma

AU - Clarke, Bryce

AU - Johnson, Michael

AU - Songa, Maurine

AU - Wang, Vincent

AU - Zardini, Gioele

N1 - Copyright © Chollet, Clarke, Johnson, Songa, Wang, Zardini. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

PY - 2022/11/3

Y1 - 2022/11/3

N2 - Lenses are an important tool in applied category theory. While individual lenses have been widely used in applications, many of the mathematical properties of the corresponding categories of lenses have remained unknown. In this paper, we study the category of small categories and asymmetric delta lenses, and prove that it has several good exactness properties. These properties include the existence of certain limits and colimits, as well as so-called imported limits, such as imported products and imported pullbacks, which have arisen previously in applications. The category is also shown to be extensive, and it has an image factorisation system.

AB - Lenses are an important tool in applied category theory. While individual lenses have been widely used in applications, many of the mathematical properties of the corresponding categories of lenses have remained unknown. In this paper, we study the category of small categories and asymmetric delta lenses, and prove that it has several good exactness properties. These properties include the existence of certain limits and colimits, as well as so-called imported limits, such as imported products and imported pullbacks, which have arisen previously in applications. The category is also shown to be extensive, and it has an image factorisation system.

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AN - SCOPUS:85142927351

T3 - Electronic Proceedings in Theoretical Computer Science, EPTCS

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BT - Proceedings of the Fourth International Conference on Applied Category Theory

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T2 - 4th International Conference on Applied Category Theory, ACT 2021

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ER -

Limits and colimits in a category of lenses

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