• Coherent Presentations of Mono...

Treffer: Coherent Presentations of Monoidal Categories

Title:
Coherent Presentations of Monoidal Categories
Authors:
Curien, Pierre-Louis, Mimram, Samuel
Contributors:
Institut de Recherche en Informatique Fondamentale (IRIF (UMR_8243)), Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Design, study and implementation of languages for proofs and programs (PI.R2), Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche en Informatique Fondamentale (IRIF (UMR_8243)), Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Centre Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire d'informatique de l'École polytechnique [Palaiseau] (LIX), École polytechnique (X), Institut Polytechnique de Paris (IP Paris)-Institut Polytechnique de Paris (IP Paris)-Centre National de la Recherche Scientifique (CNRS), ANR-13-BS02-0005,CATHRE,Catégories, Homotopie et Réécriture(2013)
Source:
Logical Methods in Computer Science. 13(3):1-38
Publisher Information:
CCSD; Logical Methods in Computer Science Association, 2017.
Publication Year:
2017
Collection:
collection:UNIV-PARIS7
collection:X
collection:CNRS
collection:INRIA
collection:INRIA-ROCQ
collection:LIX
collection:X-LIX
collection:X-DEP
collection:X-DEP-INFO
collection:LORIA2
collection:TESTALAIN1
collection:INRIA2
collection:USPC
collection:UNIV-PARIS-SACLAY
collection:X-SACLAY
collection:INRIA2017
collection:UNIV-PARIS
collection:UP-SCIENCES
collection:ANR
collection:INRIAARTDOI
collection:IRIF
collection:DEPARTEMENT-DE-MATHEMATIQUES
Subject Terms:
ACM: F.: Theory of Computation, F.4: MATHEMATICAL LOGIC AND FORMAL LANGUAGES, F.4.2: Grammars and Other Rewriting Systems, [INFO.INFO-LO]Computer Science [cs], Logic in Computer Science [cs.LO], [MATH.MATH-CT]Mathematics [math], Category Theory [math.CT]
Original Identifier:
ARXIV: 1705.03553
HAL: hal-01662524
Document Type:
Zeitschrift article<br />Journal articles
Language:
English
ISSN:
1860-5974
Relation:
info:eu-repo/semantics/altIdentifier/arxiv/1705.03553; info:eu-repo/semantics/altIdentifier/doi/10.23638/LMCS-13(3:31)2017
DOI:
10.23638/LMCS-13(3:31)2017
Access URL:
https://inria.hal.science/hal-01662524
https://inria.hal.science/hal-01662524v1/document
https://inria.hal.science/hal-01662524v1/file/1705.03553.pdf
Rights:
info:eu-repo/semantics/OpenAccess
URL: http://creativecommons.org/licenses/by/
Accession Number:
edshal.hal.01662524v1
Database:
HAL

Weitere Informationen

Presentations of categories are a well-known algebraic tool to provide descriptions of categories by means of generators, for objects and morphisms, and relations on morphisms. We generalize here this notion, in order to consider situations where the objects are considered modulo an equivalence relation, which is described by equational generators. When those form a convergent (abstract) rewriting system on objects, there are three very natural constructions that can be used to define the category which is described by the presentation: one consists in turning equational generators into identities (i.e. considering a quotient category), one consists in formally adding inverses to equational generators (i.e. localizing the category), and one consists in restricting to objects which are normal forms. We show that, under suitable coherence conditions on the presentation, the three constructions coincide, thus generalizing celebrated results on presentations of groups, and we extend those conditions to presentations of monoidal categories.