We provide an internal characterization of the category Cpo of complete posets and continuous functions within the model H of SDT recently introduced by the authors It follows that cpos lie between the two extreme synthetic notions of domain given by repleteness and well completeness

We study the so-called “Smith is Huq” condition in the context of Sprotomodular categories: two S-equivalence relations centralise each other if and only if their normalisations commute. We prove that this condition is satisfied by every category of monoids with operations equipped with the class S of Schreier split epimorphisms. Some consequences in terms of characterisation of internal struct...

1 Tensor Categories 4 Extending ̋ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Invertible objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Internal Hom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Rigid tensor categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Tensor functors . . . . ...

We define and systematically study nonassociative C *-algebras as C *-algebras internal to a topological tensor category. We also offer a concrete approach to these C *-algebras, as G-invariant, norm closed *-subalgebras of bounded operators on a G-Hilbert space, with deformed composition product. Our central results are those of stabilization and Takai duality for (twisted) crossed products in...

The definition and calculus of extraordinary natural transformations [EK] is extended to a context internal to any autonomous monoidal bicategory [DyS]. The original calculus is recaptured from the geometry [SV], [MT] of the monoidal bicategory V-Mod whose objects are categories enriched in a cocomplete symmetric monoidal category V and whose morphisms are modules. Mathematics Subject Classific...

We give various internal descriptions of the category !-Cpo of !-complete posets and !-continuous functions in the model H of Synthetic Domain Theory introduced in 8]. It follows that the !-cpos lie between the two extreme synthetic notions of domain given by repleteness and well-completeness.

In the context of Mal’cev categories, a left exact root for the congruence distributive property is given and investigated, namely the property that there is no non trivial internal group inside the fibres of the fibration of pointed objects. Indeed, when moreover the basic category C is Barr exact, the two previous properties are shown to be equivalent.

in this paper we construct the category of coverings of fundamental generalized lie group-groupoid associatedwith a connected generalized lie group. we show that this category is equivalent to the category of coverings of aconnected generalized lie group. in addition, we prove the category of coverings of generalized lie groupgroupoidand the category of actions of this generalized lie group-gro...

We present a solution to the problem of defining a counterpart in Algebraic Set Theory of the construction of internal sheaves in Topos Theory. Our approach is general in that we consider sheaves as determined by Lawvere-Tierney coverages, rather than by Grothendieck coverages, and assume only a weakening of the axioms for small maps originally introduced by Joyal and Moerdijk, thus subsuming t...