Arboreal Categories: An Axiomatic Theory of Resources

Game comonads provide a categorical syntax-free approach to finite model theory, and their Eilenberg-Moore coalgebras typically encode important combinatorial parameters of structures. In this paper, we develop a framework whereby the essential properties of these categories of coalgebras are captur...

Full description

Saved in:
Bibliographic Details
Published in:Logical methods in computer science Vol. 19, Issue 3
Main Authors: Abramsky, Samson, Reggio, Luca
Format: Journal Article
Language:English
Published: Logical Methods in Computer Science e.V 10.08.2023
Subjects:
computer science - logic in computer science
mathematics - category theory
mathematics - logic
ISSN:1860-5974, 1860-5974
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract Game comonads provide a categorical syntax-free approach to finite model theory, and their Eilenberg-Moore coalgebras typically encode important combinatorial parameters of structures. In this paper, we develop a framework whereby the essential properties of these categories of coalgebras are captured in a purely axiomatic fashion. To this end, 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 general, axiomatic setting, and applied to relational structures, where the comonadic constructions for pebbling, Ehrenfeucht-Fra\"iss\'e and modal bisimulation games recently introduced by Abramsky et al. are recovered, showing that many of the fundamental notions of finite model theory and descriptive complexity arise from instances of arboreal covers.
AbstractList Game comonads provide a categorical syntax-free approach to finite model theory, and their Eilenberg-Moore coalgebras typically encode important combinatorial parameters of structures. In this paper, we develop a framework whereby the essential properties of these categories of coalgebras are captured in a purely axiomatic fashion. To this end, 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 general, axiomatic setting, and applied to relational structures, where the comonadic constructions for pebbling, Ehrenfeucht-Fra\"iss\'e and modal bisimulation games recently introduced by Abramsky et al. are recovered, showing that many of the fundamental notions of finite model theory and descriptive complexity arise from instances of arboreal covers.
Game comonads provide a categorical syntax-free approach to finite model theory, and their Eilenberg-Moore coalgebras typically encode important combinatorial parameters of structures. In this paper, we develop a framework whereby the essential properties of these categories of coalgebras are captured in a purely axiomatic fashion. To this end, 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 general, axiomatic setting, and applied to relational structures, where the comonadic constructions for pebbling, Ehrenfeucht-Fra\"iss\'e and modal bisimulation games recently introduced by Abramsky et al. are recovered, showing that many of the fundamental notions of finite model theory and descriptive complexity arise from instances of arboreal covers.
Author Abramsky, Samson
Reggio, Luca
Author_xml – sequence: 1
  givenname: Samson
  surname: Abramsky
  fullname: Abramsky, Samson
– sequence: 2
  givenname: Luca
  surname: Reggio
  fullname: Reggio, Luca
BookMark eNpNkE1LAzEURYNUsNb-AVez1MVoXpLJJN0NxY9CQZC6DknmpU6ZNpJUsP_eaRXxbt7lLQ6Xc0lGu7hDQq6B3gnJtLrvtz6XoG_4DMQto4yfkTEoSctK12L0r1-Qac4bOoRzUEyOSdUkFxPavpjbPa5j6jDPimZXNF9d3Np954vVO8Z0KGIoXjHHz-QxX5HzYPuM0987IW-PD6v5c7l8eVrMm2XpGeO89IBS2BprRQW3XgVwGim0NSohHIYqSFnTYa8KiIxp3wYGLQWmLW25VXxCFj_cNtqN-Ujd1qaDibYzp0dMa2PTsLFH45QHB7SijDlBLbdWB6aD5EJWtA5uYLEflk8x54ThjwfUnDyao0cD2nADwhw98m9YI2cQ
ContentType Journal Article
DBID AAYXX
CITATION
DOA
DOI 10.46298/lmcs-19(3:14)2023
DatabaseName CrossRef
DOAJ Directory of Open Access Journals
DatabaseTitle CrossRef
DatabaseTitleList CrossRef
Database_xml – sequence: 1
  dbid: DOA
  name: DOAJ Directory of Open Access Journals
  url: https://www.doaj.org/
  sourceTypes: Open Website
DeliveryMethod fulltext_linktorsrc
Discipline Computer Science
EISSN 1860-5974
ExternalDocumentID oai_doaj_org_article_b8c1b105022b40a3aa9f29f6346507fb
10_46298_lmcs_19_3_14_2023
GroupedDBID .4S
.DC
29L
2WC
5GY
5VS
AAFWJ
AAYXX
ADBBV
ADMLS
ADQAK
AENEX
AFPKN
ALMA_UNASSIGNED_HOLDINGS
ARCSS
BCNDV
CITATION
EBS
EJD
FRP
GROUPED_DOAJ
J9A
KQ8
MK~
ML~
M~E
OK1
OVT
P2P
TR2
TUS
XSB
ID FETCH-LOGICAL-c2233-c1e64a7e78043ac8f1b9e01d7e844bef5f66700238fee229cdf21d0129a0d3a83
IEDL.DBID DOA
ISSN 1860-5974
IngestDate Fri Oct 03 12:41:25 EDT 2025
Sat Nov 29 06:21:52 EST 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c2233-c1e64a7e78043ac8f1b9e01d7e844bef5f66700238fee229cdf21d0129a0d3a83
OpenAccessLink https://doaj.org/article/b8c1b105022b40a3aa9f29f6346507fb
ParticipantIDs doaj_primary_oai_doaj_org_article_b8c1b105022b40a3aa9f29f6346507fb
crossref_primary_10_46298_lmcs_19_3_14_2023
PublicationCentury 2000
PublicationDate 2023-08-10
PublicationDateYYYYMMDD 2023-08-10
PublicationDate_xml – month: 08
  year: 2023
  text: 2023-08-10
  day: 10
PublicationDecade 2020
PublicationTitle Logical methods in computer science
PublicationYear 2023
Publisher Logical Methods in Computer Science e.V
Publisher_xml – name: Logical Methods in Computer Science e.V
SSID ssj0000331826
Score 2.3402529
Snippet Game comonads provide a categorical syntax-free approach to finite model theory, and their Eilenberg-Moore coalgebras typically encode important combinatorial...
Game comonads provide a categorical syntax-free approach to finite model theory, and their Eilenberg-Moore coalgebras typically encode important combinatorial...
SourceID doaj
crossref
SourceType Open Website
Index Database
SubjectTerms computer science - logic in computer science
mathematics - category theory
mathematics - logic
Title Arboreal Categories: An Axiomatic Theory of Resources
URI https://doaj.org/article/b8c1b105022b40a3aa9f29f6346507fb
Volume 19, Issue 3
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVAON
  databaseName: DOAJ Directory of Open Access Journals
  customDbUrl:
  eissn: 1860-5974
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000331826
  issn: 1860-5974
  databaseCode: DOA
  dateStart: 20040101
  isFulltext: true
  titleUrlDefault: https://www.doaj.org/
  providerName: Directory of Open Access Journals
– providerCode: PRVHPJ
  databaseName: ROAD: Directory of Open Access Scholarly Resources
  customDbUrl:
  eissn: 1860-5974
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000331826
  issn: 1860-5974
  databaseCode: M~E
  dateStart: 20040101
  isFulltext: true
  titleUrlDefault: https://road.issn.org
  providerName: ISSN International Centre
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV07SwNBEF4kWNj4FuOLLSwUOXL7uMemO0OChQYLhXTLPiGgF0miWPnb3dm7SKxsbK44lmP55m7n-4abbxC6tFSx1OZZ4rVhQaBAoYlqlejCWZpam-k0NgrfF-NxOZmIx7VRX_BPWGMP3ADX06UhOpCAkGs0TxVTSngqfM544BaF13D6poVYE1PxDGYMiHPTJcNzKsrey6tZJERcsT7h1zA0_FcmWjPsj5lltIu2W0qIq2Yre2jD1ftoZzVuAbdf3wHKqnkIWCB2eAD2DjMQuX1c1bj6nM6i8ypuOu3xzONVWX5xiJ5Hw6fBXdJOPUhMSNUsMcTlXBUOnIGYMqUnWriU2MKVnGvnM59Da01Itd45SoWxnhIL9SSVWqZKdoQ69ax2xwiD-RdRxoZVjHMXwlEqywwhuaYBStJFNysE5FtjbiGDKIh4ScBLEiFZUAcS8OqiWwDpZyUYU8cbIVyyDZf8K1wn__GQU7QFG0qiM-0Z6izn7-4cbZqP5XQxv4hvQrg-fA2_AYs2t8A
linkProvider Directory of Open Access Journals
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Arboreal+Categories%3A+An+Axiomatic+Theory+of+Resources&rft.jtitle=Logical+methods+in+computer+science&rft.au=Samson+Abramsky&rft.au=Luca+Reggio&rft.date=2023-08-10&rft.pub=Logical+Methods+in+Computer+Science+e.V&rft.eissn=1860-5974&rft.volume=19%2C+Issue+3&rft_id=info:doi/10.46298%2Flmcs-19%283%3A14%292023&rft.externalDBID=DOA&rft.externalDocID=oai_doaj_org_article_b8c1b105022b40a3aa9f29f6346507fb
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1860-5974&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1860-5974&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1860-5974&client=summon