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DOI: 10.4230/LIPIcs.ICALP.2021.115
URN: urn:nbn:de:0030-drops-141845
URL: https://drops.dagstuhl.de/opus/volltexte/2021/14184/
Abramsky, Samson ; Reggio, Luca
Arboreal Categories and Resources
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Abstract
We introduce arboreal categories, which have an intrinsic process structure, allowing dynamic notions such as bisimulation and back-and-forth games, and resource notions such as number of rounds of a game, to be defined. These are related to extensional or "static" structures via arboreal covers, which are resource-indexed comonadic adjunctions. These ideas are developed in a very general, axiomatic setting, and applied to relational structures, where the comonadic constructions for pebbling, Ehrenfeucht-Fraïssé and modal bisimulation games recently introduced in [Abramsky et al., 2017; S. Abramsky and N. Shah, 2018; Abramsky and Shah, 2021] are recovered, showing that many of the fundamental notions of finite model theory and descriptive complexity arise from instances of arboreal covers.
BibTeX - Entry
@InProceedings{abramsky_et_al:LIPIcs.ICALP.2021.115,
author = {Abramsky, Samson and Reggio, Luca},
title = {{Arboreal Categories and Resources}},
booktitle = {48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
pages = {115:1--115:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-195-5},
ISSN = {1868-8969},
year = {2021},
volume = {198},
editor = {Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/14184},
URN = {urn:nbn:de:0030-drops-141845},
doi = {10.4230/LIPIcs.ICALP.2021.115},
annote = {Keywords: factorisation system, embedding, comonad, coalgebra, open maps, bisimulation, game, resources, relational structures, finite model theory}
}
| Keywords: | factorisation system, embedding, comonad, coalgebra, open maps, bisimulation, game, resources, relational structures, finite model theory | |
| Seminar: | 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021) | |
| Issue date: | 2021 | |
| Date of publication: | 02.07.2021 |
