Topical categories of domains Export

@article{citeulike:4643250, abstract = {This paper shows how it is possible to express many techniques of categorical domain theory in the general context of topical categories (where \‘topical\’ means internal in the category Top of Grothendieck toposes with geometric morphisms). The underlying topos machinery is hidden by using a geometric form of constructive mathematics, which enables toposes as \‘generalized topological spaces\’ to be treated in a transparently spatial way, and also shows the constructivity of the arguments. The theory of strongly algebraic (SFP) domains is given as a case study in which the topical category is Cartesian closed.}, address = {New York, NY, USA}, author = {Vickers, Steven}, citeulike-article-id = {4643250}, citeulike-linkout-0 = {http://portal.acm.org/citation.cfm?id=967046}, citeulike-linkout-1 = {http://dx.doi.org/10.1017/S0960129599002741}, doi = {10.1017/S0960129599002741}, issn = {0960-1295}, journal = {Mathematical. Structures in Comp. Sci.}, keywords = {algebraicity, algebras, category-theory, constructivity, domain-theory, domains, fol, geometricity, locales, stone-duality, topological-spaces, topos-theory, toposes}, number = {5}, pages = {569--616}, posted-at = {2009-05-27 11:14:06}, priority = {2}, publisher = {Cambridge University Press}, title = {Topical categories of domains}, url = {http://dx.doi.org/10.1017/S0960129599002741}, volume = {9}, year = {1999} }

TY - JOUR ID - citeulike:4643250 L3 - citeulike-article-id:4643250 N2 - This paper shows how it is possible to express many techniques of categorical domain theory in the general context of topical categories (where ‘topical’ means internal in the category Top of Grothendieck toposes with geometric morphisms). The underlying topos machinery is hidden by using a geometric form of constructive mathematics, which enables toposes as ‘generalized topological spaces’ to be treated in a transparently spatial way, and also shows the constructivity of the arguments. The theory of strongly algebraic (SFP) domains is given as a case study in which the topical category is Cartesian closed. IS - 5 JF - Mathematical. Structures in Comp. Sci. SN - 0960-1295 AD - New York, NY, USA EP - 616 TI - Topical categories of domains PB - Cambridge University Press VL - 9 SP - 569 KW - algebraicity KW - algebras KW - category-theory KW - constructivity KW - domain-theory KW - domains KW - fol KW - geometricity KW - locales KW - stone-duality KW - topological-spaces KW - topos-theory KW - toposes AU - Vickers, Steven PY - 1999/// UR - http://dx.doi.org/10.1017/S0960129599002741 ER -