Characterizing Van Kampen Squares via Descent Data
Categories in which cocones satisfy certain exactness conditions w.r.t. pullbacks are subject to current research activities in theoretical computer science. Usually, exactness is expressed in terms of properties of the pullback functor associated with the cocone. Even in the case of non-exactness,...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Open Publishing Association
2012-08-01
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| Series: | Electronic Proceedings in Theoretical Computer Science |
| Online Access: | http://arxiv.org/pdf/1209.1435v1 |
| _version_ | 1818972894199283712 |
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| author | Harald König Uwe Wolter Michael Löwe |
| author_facet | Harald König Uwe Wolter Michael Löwe |
| author_sort | Harald König |
| collection | DOAJ |
| description | Categories in which cocones satisfy certain exactness conditions w.r.t. pullbacks are subject to current research activities in theoretical computer science. Usually, exactness is expressed in terms of properties of the pullback functor associated with the cocone. Even in the case of non-exactness, researchers in model semantics and rewriting theory inquire an elementary characterization of the image of this functor. In this paper we will investigate this question in the special case where the cocone is a cospan, i.e. part of a Van Kampen square. The use of Descent Data as the dominant categorical tool yields two main results: A simple condition which characterizes the reachable part of the above mentioned functor in terms of liftings of involved equivalence relations and (as a consequence) a necessary and sufficient condition for a pushout to be a Van Kampen square formulated in a purely algebraic manner. |
| first_indexed | 2024-12-20T15:15:31Z |
| format | Article |
| id | doaj.art-6f13622edb3748bb853dc632c8248817 |
| institution | Directory Open Access Journal |
| issn | 2075-2180 |
| language | English |
| last_indexed | 2024-12-20T15:15:31Z |
| publishDate | 2012-08-01 |
| publisher | Open Publishing Association |
| record_format | Article |
| series | Electronic Proceedings in Theoretical Computer Science |
| spelling | doaj.art-6f13622edb3748bb853dc632c82488172022-12-21T19:36:11ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802012-08-0193Proc. ACCAT 2012618110.4204/EPTCS.93.4Characterizing Van Kampen Squares via Descent DataHarald KönigUwe WolterMichael LöweCategories in which cocones satisfy certain exactness conditions w.r.t. pullbacks are subject to current research activities in theoretical computer science. Usually, exactness is expressed in terms of properties of the pullback functor associated with the cocone. Even in the case of non-exactness, researchers in model semantics and rewriting theory inquire an elementary characterization of the image of this functor. In this paper we will investigate this question in the special case where the cocone is a cospan, i.e. part of a Van Kampen square. The use of Descent Data as the dominant categorical tool yields two main results: A simple condition which characterizes the reachable part of the above mentioned functor in terms of liftings of involved equivalence relations and (as a consequence) a necessary and sufficient condition for a pushout to be a Van Kampen square formulated in a purely algebraic manner.http://arxiv.org/pdf/1209.1435v1 |
| spellingShingle | Harald König Uwe Wolter Michael Löwe Characterizing Van Kampen Squares via Descent Data Electronic Proceedings in Theoretical Computer Science |
| title | Characterizing Van Kampen Squares via Descent Data |
| title_full | Characterizing Van Kampen Squares via Descent Data |
| title_fullStr | Characterizing Van Kampen Squares via Descent Data |
| title_full_unstemmed | Characterizing Van Kampen Squares via Descent Data |
| title_short | Characterizing Van Kampen Squares via Descent Data |
| title_sort | characterizing van kampen squares via descent data |
| url | http://arxiv.org/pdf/1209.1435v1 |
| work_keys_str_mv | AT haraldkonig characterizingvankampensquaresviadescentdata AT uwewolter characterizingvankampensquaresviadescentdata AT michaellowe characterizingvankampensquaresviadescentdata |