Coequations and Eilenberg–type Correspondences

[1]  Chung-Kil Hur,et al.  Equational Systems and Free Constructions (Extended Abstract) , 2007, ICALP.

[2]  Marcello M. Bonsangue,et al.  Equations and Coequations for Weighted Automata , 2015, MFCS.

[3]  Jirí Adámek.  A Logic of Coequations , 2005, CSL.

[4]  Mikolaj Bojanczyk,et al.  Recognisable Languages over Monads , 2015, DLT.

[5]  Robert Goldblatt,et al.  Covarieties of Coalgebras: Comonads and Coequations , 2005, ICTAC.

[6]  Jesse Hughes,et al.  Modal Operators and the Formal Dual of Birkhoff's Completeness Theorem , 2003, Math. Struct. Comput. Sci..

[7]  Jan Reiterman,et al.  The Birkhoff theorem for finite algebras , 1982 .

[8]  B. Jacobs,et al.  A tutorial on (co)algebras and (co)induction , 1997 .

[9]  Jesse Hughes,et al.  A study of categories of algebras and coalgebras , 2001 .

[10]  H. Peter Gumm.  Equational and implicational classes of coalgebras , 2001, Theor. Comput. Sci..

[11]  George Gratzer,et al.  Universal Algebra , 1979 .

[12]  Jurriaan Rot,et al.  Duality of Equations and Coequations via Contravariant Adjunctions , 2016, CMCS.

[13]  G. Birkhoff,et al.  On the Structure of Abstract Algebras , 1935 .

[14]  J. Wright,et al.  P-varieties - a signature independent characterization of varieties of ordered algebras , 1983 .

[15]  Jiří Adámek.  Birkhoff's Covariety Theorem without limitations , 2005 .

[16]  H. Herrlich,et al.  Identities in Categories , 1972, Canadian Mathematical Bulletin.

[17]  MICHAEL BARR.  HSP SUBCATEGORIES OF EILENBERG-MOORE ALGEBRAS , 2002 .

[18]  Bartek Klin,et al.  Coalgebraic Modal Logic Beyond Sets , 2007, MFPS.

[19]  Stefan Milius,et al.  Generalized Eilenberg Theorem I: Local Varieties of Languages , 2014, FoSSaCS.

[20]  John T. Baldwin,et al.  Varieties and finite closure conditions , 1976 .

[21]  STEPHrN L. BLOOM,et al.  Varieties of Ordered Algebras , 1976, J. Comput. Syst. Sci..

[22]  Mai Gehrke.  Stone Duality and the Recognisable Languages over an Algebra , 2009, CALCO.

[23]  Bart Jacobs,et al.  Structural Induction and Coinduction in a Fibrational Setting , 1998, Inf. Comput..

[24]  Jurriaan Rot,et al.  Coalgebraic Trace Semantics via Forgetful Logics , 2015, FoSSaCS.

[25]  Libor Polák.  Syntactic Semiring of a Language , 2001, MFCS.

[26]  Murdoch James Gabbay.  Nominal Algebra and the HSP Theorem , 2009, J. Log. Comput..

[27]  Michael Barr.  Duality of vector spaces , 1976 .

[28]  Horst Herrlich,et al.  Abstract and concrete categories , 1990 .

[29]  Alexander Kurz,et al.  Operations and equations for coalgebras , 2005, Mathematical Structures in Computer Science.

[30]  Jacques Sakarovitch,et al.  Elements of Automata Theory , 2009 .

[31]  H. Peter Gumm,et al.  Covarieties and Complete Covarieties , 1998, CMCS.

[32]  Andrzej Tarlecki,et al.  Some Nuances of Many-sorted Universal Algebra: A Review , 2011, Bull. EATCS.

[33]  Symeon Bozapalidis,et al.  On the recognizability of Fuzzy languages I , 2006, Fuzzy Sets Syst..

[34]  Alexander Kurz,et al.  On universal algebra over nominal sets , 2010, Math. Struct. Comput. Sci..

[35]  Marcello M. Bonsangue,et al.  Duality for Logics of Transition Systems , 2005, FoSSaCS.

[36]  P. T. Johnstone,et al.  Adjoint Lifting Theorems for Categories of Algebras , 1975 .

[37]  Jurriaan Rot,et al.  Presenting Distributive Laws , 2013, CALCO.

[38]  Michael W. Mislove,et al.  The Pontryagin Duality of Compact O-Dimensional Semilattices and Its Applications , 1974 .

[39]  Stefan Milius,et al.  Varieties of Languages in a Category , 2015, 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science.

[40]  James Worrell,et al.  Testing Semantics: Connecting Processes and Process Logics , 2006, AMAST.

[41]  M. Steinby.  Algebraic classifications of regular tree languages , 2005 .

[42]  Alexandra Silva,et al.  A coalgebraic perspective on linear weighted automata , 2011, Inf. Comput..

[43]  Frank Wolter,et al.  Handbook of Modal Logic, Volume 3 (Studies in Logic and Practical Reasoning) , 2006 .

[44]  Stanley Burris,et al.  A course in universal algebra , 1981, Graduate texts in mathematics.

[45]  Ana Sokolova,et al.  Exemplaric Expressivity of Modal Logics , 2010, J. Log. Comput..

[46]  A. N. Prior,et al.  Equational logic , 1968, Notre Dame J. Formal Log..

[47]  H. Peter Gumm,et al.  Coalgebraic structure from weak limit preserving functors , 2000, CMCS.

[48]  S. Lane.  Categories for the Working Mathematician , 1971 .

[49]  Murdoch James Gabbay,et al.  Nominal (Universal) Algebra: Equational Logic with Names and Binding , 2009, J. Log. Comput..

[50]  Brian A. Davey,et al.  An Introduction to Lattices and Order , 1989 .

[51]  Samuel Eilenberg,et al.  Automata, languages, and machines. A , 1974, Pure and applied mathematics.

[52]  Heinz-Peter Gumm.  Birkho s variety theorem for coalgebras , 2001 .

[53]  M. Droste,et al.  Semirings and Formal Power Series , 2009 .

[54]  F. E. J. Linton,et al.  Some Aspects of Equational Categories , 1966 .

[55]  Christophe Reutenauer.  Séries formelles et algèbres syntactiques , 1980 .

[56]  Bernhard Banaschewski,et al.  The Birkhoff Theorem for varieties of finite algebras , 1983 .

[57]  Daniel Schwencke.  Coequational logic for accessible functors , 2010, Inf. Comput..

[58]  Marcel Paul Schützenberger,et al.  On the Definition of a Family of Automata , 1961, Inf. Control..

[59]  Julian Salamanca Tellez,et al.  An Eilenberg-like theorem for algebras on a monad , 2016, FM 2016.

[60]  Jesse Hughes,et al.  The Coalgebraic Dual Of Birkhoff's Variety Theorem , 2000 .

[61]  Jan J. M. M. Rutten,et al.  The dual equivalence of equations and coequations for automata , 2014, Inf. Comput..

[62]  Marcello M. Bonsangue,et al.  Regular Varieties of Automata and Coequations , 2015, MPC.

[63]  Stefan Milius,et al.  Profinite Monads, Profinite Equations, and Reiterman's Theorem , 2015, FoSSaCS.

[64]  Julian Salamanca,et al.  Unveiling Eilenberg-type Correspondences: Birkhoff's Theorem for (finite) Algebras + Duality , 2017, ArXiv.

[65]  David M. Clark,et al.  Natural Dualities for the Working Algebraist , 1998 .

[66]  Magnus Steinby,et al.  General Varieties of Tree Languages , 1998, Theor. Comput. Sci..

[67]  Christos H. Papadimitriou,et al.  Elements of the Theory of Computation , 1997, SIGA.

[68]  Jerzy Płonka,et al.  On a method of construction of abstract algebras , 1967 .

[69]  Jean-Eric Pin,et al.  A variety theorem without complementation , 1995 .

[70]  Tatjana Petković,et al.  Varieties of fuzzy languages ? , 2005 .

[71]  Grigore Rosu.  Equational axiomatizability for coalgebra , 2001, Theor. Comput. Sci..

[72]  Serge Grigorieff,et al.  Duality and Equational Theory of Regular Languages , 2008, ICALP.

[73]  C. J Ash.  Pseudovarieties, generalized varieties and similarly described classes , 1985 .

[74]  Jan J. M. M. Rutten,et al.  Universal coalgebra: a theory of systems , 2000, Theor. Comput. Sci..