Frölicher spaces form a cartesian closed category which contains the category of smooth manifolds as a full subcategory. Therefore, mapping groups such as C∞(M, G) or Diff(M), but also projective limits of Lie groups are in a natural way objects of that category, and group operations are morphisms in the category. We call groups with this property Frölicher groups. One can define tangent spaces...

We obtain a characterization of the completion of an initial uniform convergence structure, which includes, among others, subspaces and projective limits of uniform convergence spaces. In this regard, there seems to be a gap in the literature. This characterization is obtained in a surprisingly straightforward way, and this should be viewed as a consequence of the fact that the category UCS of ...

or171algebra12, 25adapted to typed set150associated37, 43, 150, 152bottomed58category-based126containing a typed set37disjoint from a typed set46extension of46free37functionally free145, 147functional145, 147ground term56heterogenous54initial12, 33initial completion of104<...

We introduce a bicartesian closed category of what we call pro nite domains. Study of these domains is carried out through the use of an equivalent category of pre-orders in a manner similar to the information systems approach advocated by Dana Scott and others. A class of universal pro nite domains is de ned and used to derive su cient conditions for the pro nite solution of domain equations i...

Sheaves are objects of a local nature: a global section is determined by how it looks locally. Hence, a sheaf cannot describe mathematical structures which contain global or nonlocal geometric information. To fill this gap, we introduce the theory of “gleaves”, which are presheaves equipped with an additional “gluing operation” of compatible pairs of local sections. This generalizes the conditi...

The category of flows is not cartesian closed. We construct a closed symmetric monoidal structure which has moreover a satisfactory behavior from the computer scientific viewpoint.

Semiuniform convergence spaces form a common generalization of lter spaces (including symmetric convergence spaces and thus symmetric topological spaces] as well as Cauchy spaces) and uniform limit spaces (including uniform spaces) with many convenient properties such as cartesian closedness, hereditariness and the fact that products of quotients are quotients. Here, for each semiuniform conver...

A conjecture of Smyth is discussed which says that if D and [D → D] are effectively algebraic directed-complete partial orders with least element (cpo’s), then D is an effectively strongly algebraic cpo, where it was not made precise what is meant by an effectively algebraic and an effectively strongly algebraic cpo. Notions of an effectively strongly algebraic cpo and an effective SFP domain a...

We prove that every finitary polynomial endofunctor of a category C has a final coalgebra if C is locally Cartesian closed, has finite disjoint coproducts and a natural number object. More generally, we prove that the category of coalgebras for such an endofunctor has all finite limits.

Suppose in an arithmetic unverse we have two predicates φ and ψ for natural numbers, satisfying a base case φ(0) → ψ(0) and an induction step that, for generic n, the hypothesis φ(n) → ψ(n) allows one to deduce φ(n+ 1) → ψ(n+ 1). Then it is already true in that arithmetic universe that (∀n)(φ(n) → ψ(n)). This is substantially harder than in a topos, where cartesian closedness allows one to form...