Comonads, Coequations and Behavioural Covarieties Export

@mastersthesis{citeulike:566405, abstract = {Coalgebras are a category theoretic computer science, defined by an endofunctor T : C --> C over a category C. A class K of T-coalgebras is a covariety if it is closed under coproducts, codomains of epi coalgebraic morphisms and subcoalgebras, and a behavioural covariety if it is closed under images of bisimulations. Often the forgetful functor from the category of T-coalgebras to C has a right adjoint. This adjunction defines a comoad G^T. Goldblatt [11] investigated this situation oven the category Set, introducing the notion of a pure subcomonad of a comonad, and showing a bijective correspondence between (equivalence classes of) pure subcomonads of G^T and behavioural covarieties of T-coalgebras. This thesis demonstrates what restrictions need to be applied to an arbitrary category C and endofunctor T : C --> C to attain this bijection. All restrictions on C and T are shown to apply to an endofunctor ()^I on a sategory Set^\sub that is useful for modelling automata. The thesis goes on to show that pure subcomonads give rise to subcoalgebras of the final coalgebra called coequations over 1, and demonstrates a bijective correspondence between behavioural covarieties of T-coalgebras and coequations over 1. Finally the thesis shows that, given an extra assumption on C, there is a bijective correspondence between covarieties of T-coalgebras and a class of subcomonads called regulating subcomonads.}, author = {Clouston, Ranald}, citeulike-article-id = {566405}, keywords = {coalgebra, coequation, comonad, covariety, thesis-msc}, posted-at = {2006-03-28 03:16:40}, priority = {0}, school = {Victoria University of Wellington}, title = {Comonads, Coequations and Behavioural Covarieties}, year = {2004} }

TY - THES ID - citeulike:566405 L3 - citeulike-article-id:566405 N2 - Coalgebras are a category theoretic computer science, defined by an endofunctor T : C --> C over a category C. A class K of T-coalgebras is a covariety if it is closed under coproducts, codomains of epi coalgebraic morphisms and subcoalgebras, and a behavioural covariety if it is closed under images of bisimulations. Often the forgetful functor from the category of T-coalgebras to C has a right adjoint. This adjunction defines a comoad G^T. Goldblatt [11] investigated this situation oven the category Set, introducing the notion of a pure subcomonad of a comonad, and showing a bijective correspondence between (equivalence classes of) pure subcomonads of G^T and behavioural covarieties of T-coalgebras. This thesis demonstrates what restrictions need to be applied to an arbitrary category C and endofunctor T : C --> C to attain this bijection. All restrictions on C and T are shown to apply to an endofunctor ()^I on a sategory Set^\sub that is useful for modelling automata. The thesis goes on to show that pure subcomonads give rise to subcoalgebras of the final coalgebra called coequations over 1, and demonstrates a bijective correspondence between behavioural covarieties of T-coalgebras and coequations over 1. Finally the thesis shows that, given an extra assumption on C, there is a bijective correspondence between covarieties of T-coalgebras and a class of subcomonads called regulating subcomonads. TI - Comonads, Coequations and Behavioural Covarieties PB - Victoria University of Wellington KW - coalgebra KW - coequation KW - comonad KW - covariety KW - thesis-msc AU - Clouston, Ranald PY - 2004/// ER -