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A comonadic account of behavioural covarieties of coalgebras

2005
*
Mathematical Structures in Computer Science
*

Then we show that

doi:10.1017/s096012950400458x
fatcat:g5aflvvy4rbkhoa45l7d3dnina
*behavioural**covarieties*K are (isomorphic to) the Eilenberg-Moore categories*of**coalgebras*for certain*comonads*G K naturally associated with G T . ... We show that there is*a*bijective correspondence between*behavioural**covarieties**of*T -*coalgebras*and isomorphism classes*of*pure subcomonads*of*G T . ... Thus*a*categorical*account**of**behavioural**covarieties*closed under ultrafilter enlargements will need to analyse the relationship between*a*monad and*a**comonad*, and is*a*natural topic for further study ...##
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Covarieties of Coalgebras: Comonads and Coequations
[chapter]

2005
*
Lecture Notes in Computer Science
*

We identify conditions on the underlying category

doi:10.1007/11560647_19
fatcat:5qu67cnmxva7xfat2d2sb575xi
*of**a**comonad*G which ensure that there is an exact correspondence between (*behavioural*/virtual)*covarieties**of*G-*coalgebras*and subcomonads*of*G defined ...*A*virtual*covariety*is*a*class*of**coalgebras*closed under coproducts, images*of**coalgebraic*morphisms, and subcoalgebras defined by split equalisers. ... The authors acknowledge support from*a*Logic and Computation programme funded by the New Zealand Institute*of*Mathematics and its Applications. ...##
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Modal Predicates and Coequations

2002
*
Electronical Notes in Theoretical Computer Science
*

We prove

doi:10.1016/s1571-0661(04)80364-5
fatcat:44m54cet3vaitf3g27szekzvt4
*a*general co-Birkhoff theorem describing*covarieties**of**coalgebras*by means*of*coequations. We argue that the resulting coequational logic generalises modal logic. ... This is*a*special case*of*Linton's approach to algebras over*a*general base category X , namely where X is taken as the dual*of*sets. ... We define two notions, the second one taking 'colourings' into*account*: Given C,*a*colouring v for*a**coalgebra**A*is an arrow U*A*→ C. ...##
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How to write a coequation
[article]

2021
*
arXiv
*
pre-print

There is

arXiv:2109.11967v1
fatcat:gjiohhvtfvhrhnbgwzpqiatvoa
*a*large amount*of*literature on the topic*of**covarieties*, coequations and coequational specifications, dating back to the early seventies. ... We present each*of*these in*a*tutorial fashion, relate them to each other, and discuss their respective uses. ... By theorem 4.5, the*covariety**of*sequence*coalgebras*is determined by*a*set W seq*of**behaviours*. ...##
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On Specification Logics for Algebra-Coalgebra Structures: Reconciling Reachability and Observability
[chapter]

2002
*
Lecture Notes in Computer Science
*

The two frameworks are then integrated in order to

doi:10.1007/3-540-45931-6_7
fatcat:o4ggwwrhnjdpdoqhgk4xcwyk7i
*account*for structures comprising both*a**coalgebraic*(observational) component and an algebraic (computational) component. ... The integration results in logics whose sentences are either*coalgebraic*(modal) or algebraic (equational) in nature, but whose associated notions*of*satisfaction take into*account*both the*coalgebraic*... Then,*a*second goal*of*the paper is to integrate the resulting frameworks in order to*account*for structures having both*a**coalgebraic*and an algebraic component. ...##
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Algebra, coalgebra, and minimization in polynomial differential equations
[article]

2019
*
arXiv
*
pre-print

We consider reasoning and minimization in systems

arXiv:1710.08350v3
fatcat:y3voaiqulrawzoc3lecan7xmyy
*of*polynomial ordinary differential equations (ode's). The ring*of*multivariate polynomials is employed as*a*syntax for denoting system*behaviours*. ...*of**a*user-specified template. ... How to characterise such*covariety*more explicitly, for example in terms*of**comonads*, is left for future research. ...##
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Algebra, Coalgebra, and Minimization in Polynomial Differential Equations
[chapter]

2017
*
Lecture Notes in Computer Science
*

We consider reasoning and minimization in systems

doi:10.1007/978-3-662-54458-7_5
fatcat:q4qypnm43zfdzchmpg5yfyzlhq
*of*polynomial ordinary differential equations (ode's). The ring*of*multivariate polynomials is employed as*a*syntax for denoting system*behaviours*. ...*of**a*user-specified template. ... How to characterise such*covariety*more explicitly, for example in terms*of**comonads*, is left for future research. ...##
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How to Write a Coequation ((Co)algebraic pearls)

2021

There is

doi:10.4230/lipics.calco.2021.13
fatcat:2cih67o7rzgydmv7v3urjsaobm
*a*large amount*of*literature on the topic*of**covarieties*, coequations and coequational specifications, dating back to the early seventies. ... We present each*of*these in*a*tutorial fashion, relate them to each other, and discuss their respective uses. ... By Theorem 12, the*covariety**of*sequence*coalgebras*is determined by*a*set W seq*of**behaviours*. ...##
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Interpreted systems and Kripke models for multiagent systems from a categorical perspective

2004
*
Theoretical Computer Science
*

This equivalence is exploited in

doi:10.1016/j.tcs.2004.04.005
fatcat:wjeigxwv45dbpprbeuert4musa
*a*discussion*of*colimits*of*interpreted systems. ... This paper enriches previous comparisons*of*these two forms*of*semantics by considering categories*of*models in both cases and then shows that constructions given by Lomuscio and Ryan, extend to give an ... The paper has also beneÿtted from the constructive and pertinent comments*of*two referees for TCS. ...##
###
Interpreted systems and Kripke models for multiagent systems from a categorical perspective

2004
*
Theoretical Computer Science
*

This equivalence is exploited in

doi:10.1016/s0304-3975(04)00267-1
fatcat:jsfbwzm3lzdzpp5qtdbaizrwku
*a*discussion*of*colimits*of*interpreted systems. ... This paper enriches previous comparisons*of*these two forms*of*semantics by considering categories*of*models in both cases and then shows that constructions given by Lomuscio and Ryan, extend to give an ... The paper has also beneÿtted from the constructive and pertinent comments*of*two referees for TCS. ...