For Denjoy–Carleman differentiable function classes C where the weight sequence M = (Mk) is logarithmically convex, stable under derivations, and non-quasianalytic of moderate growth, we prove the following: A mapping is C if it maps C -curves to C -curves. The category of C -mappings is cartesian closed in the sense that C (E, C (F, G)) = C (E × F, G) for convenient vector spaces. Applications...

Recent works dealing with new considerations about the notion centralizer of equivalence relations gave the opportunity to reveal beyond this construction widerranging phenomenons of functorial nature which do not belong, as it is well-known, to this notion by itself. And this was done in two distinct ways: on the one hand through the notion of action accessible category [2] and on the other ha...

We define the notion of a (P, P̃ )-structure on a universe p in a locally cartesian closed category category with a binary product structure and construct a (Π, λ)-structure on the C-systems CC(C, p) from a (P, P̃ )-structure on p. We then define homomorphisms of C-systems with (Π, λ)-structures and functors of universe categories with (P, P̃ )-structures and show that our construction is functori...

We propose a semantics for permutation equivalence in higher-order rewriting. This semantics takes place in cartesian closed 2-categories, and is proved sound and complete.

BLOCKINy the construction of the PL-category in 3 directly from a given PL-category A without any reference to an ambient locally cartesian closed category L. An object in the bre over U n is a pair hT; T 0 i such that (i) T is an object in A(U n)|let t: U n-U be such that A(t)(X) = T |

The projective tensor product in a category of topologicalR-modules (where R is a topological ring) can be defined in Top, the category of topological spaces, by the same universal property used to define the tensor product of R-modules in Set. In this article, we extend this definition to an arbitrary topological category X and study how the cartesian closedness of X is related to the monoidal...

Sierpinski space Ω is injective in the category Top of topological spaces, but not in any of the larger cartesian closed categories Conv of convergence spaces and Equ of equilogical spaces. We show that this negative result extends to all sub-cccs of Equ and Conv that are closed under subspaces and contain Top. On the other hand, we study the category PrTop of pretopological spaces that lies in...

As a practical foundation for a homotopy theory of abstract spacetime, we propose a convenient category S , which we show to extend a category of certain compact partially ordered spaces. In particular, we show that S ′ is Cartesian closed and that the forgetful functor S →T ′ to the category T ′ of compactly generated spaces creates all limits and colimits.

In this paper we consider admissible domain representations of topological spaces. A domain representation D of a space X is λ-admissible if, in principle, all other λ-based domain representations E of X can be reduced to D via a continuous function from E to D. We present a characterisation theorem of when a topological space has a λ-admissible and κ-based domain representation. We also prove ...

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