Met-like categories amongst concrete topological categories

Quotient-topological completions and hulls of concrete categories

Universality of Coproducts in Categories of Lax Algebras

Categories of lax (T, V )-algebras are shown to have pullbackstable coproducts if T preserves inverse images. The general result not only gives a common proof of this property in many topological categories but also shows that important topological categories, like the category of uniform spaces, are not presentable as a category of lax (T, V )-algebras, with T preserving inverse images. Moreov...

Topological Field Theory, Higher Categories, and Their Applications

It has been common wisdom among mathematicians that Extended Topological Field Theory in dimensions higher than two is naturally formulated in terms of n-categories with n > 1. Recently the physical meaning of these higher categorical structures has been recognized and concrete examples of Extended TFTs have been constructed. Some of these examples, like the Rozansky-Witten model, are of geomet...

Classification of Concrete Geometrical Categories

A precise concept of concrete geometrical category is introduced in an axiomatic way. To any algebra L for an many-sorted infinitary algebraic theory T is associated a concrete geometrical category Geo(L), the so-called classifying concrete geometrical category of L, satisfying a universal property. The terminology "geometrical" is justified firstly for Geo(L) and secondly for any concrete geom...

- Algebras in Tensor Categories

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...