In this paper we consider Milner's calculus CCS enriched by a probabilistic choice operator. The calculus is given operational semantics based on probabilistic transition systems. We deene operational notions of preorder and equivalence as prob-abilistic extensions of the simulation preorder and the bisimulation equivalence respectively. We extend existing category-theoretic techniques for solv...

Background and Aim: The use of ceramics has a long history. A new category of these materials was used in medicine in 1960 introduced as bioceramics. Biocompatibility, osteoinductivity and sealing ability are among the most favorable characteristics of endodontic bioceramics. Introduction of mineral trioxide aggregate (MTA) revolutionized endodontics and this new era is progressively growing. ...

We outline a definition of accessible and presentable objects in 2-category K endowed with “KZ context”, that is to say pair lax-idempotent monads interacting prescribed way; this perspective suggests unified treatment many “Gabriel-Ulmer like” theorems, asserting how arise as reflections generating ones. the notion (Gabriel-Ulmer) envelope for KZ context, sufficient concoct Gabriel-Ulmer duali...

We give a correspondence between enriched categories and the Gauss-Kleene-Floyd-Warshall connection familiar to computer scientists. This correspondence shows this generalization of categories to be a close cousin to the generalization of transitive closure algorithms. Via this connection we may bring categorical and 2-categorical constructions into an active but algebraically impoverished aren...

In this work, we use Ising chain and Kitaev to check the validity of an earlier proposal in arXiv:2011.02859 that enriched fusion (higher) categories provide a unified categorical description all gapped/gapless quantum liquid phases, including symmetry-breaking topological orders, SPT/SET orders certain gapless phases. particular, show explicitly that, each gapped phase realized by these two mo...

We present a comparative study of certain invariants defined for group actions and their analogues orbifolds. In particular, we prove that Fadell's equivariant category $G$-spaces coincides with the Lusternik-Schnirelmann orbifolds when is finite.

Characterising colimiting ω-cocones of projection pairs in terms of least upper bounds of their embeddings and projections is important to the solution of recursive domain equations. We present a universal characterisation of this local property as ω-cocontinuity of locally continuous functors. We present a straightforward proof using the enriched Yoneda embedding. The proof can be generalised ...

By a multi-pointed category we mean a category C equipped with a so called ideal of null morphisms, i.e. a class N of morphisms satisfying f ∈ N ∨ g ∈ N ⇒ fg ∈ N for any composable pair f, g of morphisms. Such categories are precisely the categories enriched in the category of pairs X = (X,N) where X is a set and N is a subset of X, whereas a pointed category has the same enrichment, but restri...

Natural organized systems adapt to internal and external pressures this happens at all levels of the abstraction hierarchy. Wanting think clearly about idea motivates our paper, so is elaborated extensively in introduction, which should be broadly accessible a philosophically-interested audience. In remaining sections, we turn more compressed category theory. We define monoidal double Org dynam...