A new approach to simulations is proposed within the theory of coalgebras by taking a notion of order on a functor as primitive. Such an order forms a basic building block for a “lax relation lifting”, or “relator” as used by other authors. Simulations appear as coalgebras of this lifted functor, and similarity as greatest simulation. Two-way similarity is then similarity in both directions. In...

In this article we study a type of directed completion for posets and T0-spaces introduced by O. Wyler [Wy81] that we call the D-completion. The category D of monotone convergence spaces is a full reflective subcategory of the category of topological spaces and continuous maps, and the D-completion gives the reflection of a topological space into D, and as such exhibits a useful universal prope...

For every metric space X, we deene a continuous poset BX such that X is home-omorphic to the set of maximal elements of BX with the relative Scott topology. The poset BX is a dcpo ii X is complete, and !-continuous ii X is separable. The computational model BX is used to give domain-theoretic proofs of Banach's xed point theorem and of two classical results of Hutchinson: on a complete metric s...

We describe categorical models of a circuit-based (quantum) functional pro- gramming language. We show that enriched categories play a crucial role. Following earlier work on QWire by Paykin et al., we consider both a simple first-order linear language for circuits, and a more powerful host language, such that the circuit language is embedded inside the host language. Our categorical semantics ...

ComK may be defined as the (cartesian closed) category of comonoids in chuK , or equivalently as dictionaries D for which any crossword over D has its main diagonal in D. Com2 resembles Top, ordinary topological spaces. Common to both are the Alexandroff posets and the Scott DCPOs, while the topological space R and the dual DCPO {−∞ < . . . < −2 < −1 < 0} jointly witness the incomparability of ...

In domain theory, by a poset model of T1 topological space X we usually mean P such that the subspace Max(P) Scott consisting all maximal points is homeomorphic to X. The models spaces have been extensively studied many authors. this paper investigate another type models: lower topology models. ?(P) on one fundamental intrinsic topologies poset, which generated sets form P\?x, x ? P. A (poset L...

Abstract Working constructively, we study continuous directed complete posets (dcpos) and the Scott topology. Our two primary novelties are a notion of intrinsic apartness sharp elements. Being apart is positive formulation being unequal, similar to how inhabitedness nonemptiness. To exemplify sharpness, note that lower real if only it located. first main result for large class dcpos, Bridges–V...

This is a version from 29 Sept 2003 of the paper published under the same name in Theoretical Computer Science 316 (2004) 297–321. The double powerlocale P(X) (found by composing, in either order, the upper and lower powerlocale constructions PU and PL) is shown to be isomorphic in [Loc,Set] to the double exponential SS X where S is the Sierpiński locale. Further PU (X) and PL(X) are shown to b...