Duality for some categories of coalgebras Export

@article{citeulike:565396, abstract = {A contravariant duality is constructed between the category of coalgebras of a given signature, and a category of Boolean algebras with operators, including modal operators corresponding to state transitions in coalgebras, and distinguished elements abstracting the sets of states defined by observable equations. This duality is used to give a new proof that a class of coalgebras is definable by Boolean combinations of observable equations if it is closed under disjoint unions, domains and images of coalgebraic morphisms, and ultrafilter enlargements. The proof reduces the problem to a direct application of Birkhoff's variety theorem characterising equational classes of algebras.}, address = {Basel}, author = {Goldblatt, Robert}, citeulike-article-id = {565396}, citeulike-linkout-0 = {http://dx.doi.org/10.1007/PL00000352}, doi = {10.1007/PL00000352}, journal = {Algebra Universalis}, keywords = {coalgebra}, month = {September}, number = {3}, pages = {389--416}, posted-at = {2006-03-27 12:23:26}, priority = {0}, publisher = {Birkh\"{a}user}, title = {Duality for some categories of coalgebras}, url = {http://dx.doi.org/10.1007/PL00000352}, volume = {46}, year = {2001} }

TY - JOUR ID - citeulike:565396 L3 - citeulike-article-id:565396 N2 - A contravariant duality is constructed between the category of coalgebras of a given signature, and a category of Boolean algebras with operators, including modal operators corresponding to state transitions in coalgebras, and distinguished elements abstracting the sets of states defined by observable equations. This duality is used to give a new proof that a class of coalgebras is definable by Boolean combinations of observable equations if it is closed under disjoint unions, domains and images of coalgebraic morphisms, and ultrafilter enlargements. The proof reduces the problem to a direct application of Birkhoff's variety theorem characterising equational classes of algebras. IS - 3 JF - Algebra Universalis AD - Basel EP - 416 TI - Duality for some categories of coalgebras PB - Birkhäuser VL - 46 SP - 389 KW - coalgebra AU - Goldblatt, Robert PY - 2001/09// UR - http://dx.doi.org/10.1007/PL00000352 ER -