in this work, we describe an adjunction between the comma category of set-based monads under the v -powerset monad and the category of associative lax extensions of set-based monads to the category of v -relations. in the process, we give a general construction of the kleisli extension of a monad to the category of v-relations.

In this work, we describe an adjunction between the comma category of Set-based monads under the V -powerset monad and the category of associative lax extensions of Set-based monads to the category of V -relations. In the process, we give a general construction of the Kleisli extension of a monad to the category of V-relations.

We show that the category A(G) of actions of a locally compact group G on C∗-algebras (with equivariant nondegenerate ∗-homomorphisms into multiplier algebras) is equivalent, via a full-crossed-product functor, to a comma category of maximal coactions of G under the comultiplication (C∗(G), δG); and also that A(G) is equivalent, via a reduced-crossed-product functor, to a comma category of norm...

We construct the concrete category LiCS of left-invariant control systems (on Lie groups) and point out some very basic properties. Morphisms in this category are examined briefly. Also, covering control systems are introduced and organized into a (comma) category associated with LiCS.

In this paper we re-develop the foundations of the category theory of quasicategories (also called ∞-categories) using 2-category theory. We show that Joyal’s strict 2-category of quasi-categories admits certain weak 2-limits, among them weak comma objects. We use these comma quasi-categories to encode universal properties relevant to limits, colimits, and adjunctions and prove the expected the...

following the categorical approach to universal algebra through algebraic theories, proposed by f.~w.~lawvere in his phd thesis, this paper aims at introducing a similar setting for general topology. the cornerstone of the new framework is the notion of emph{categorically-algebraic} (emph{catalg}) emph{topological theory}, whose models induce a category of topological structures. we introduce t...

This paper tries to explain why and how category theory is useful in computing science, by giving guidelines for applying seven basic categorical concepts: category, functor, natural transformation, limit, adjoint, colimit and comma category. Some examples, intuition, and references are given for each concept, but completeness is not attempted. Some additional categorical concepts and some sugg...

Let G be a locally compact group. We show that the category A(G) of actions of G on C∗-algebras (with equivariant nondegenerate ∗-homomorphisms into multiplier algebras) is equivalent, via a full-crossed-product functor, to a comma category of maximal coactions of G under the comultiplication (C∗(G), δG); and also that A(G) is equivalent, via a reduced-crossed-product functor, to a comma catego...

We analyse the philosopher Davidson’s semantics of actions, using a strongly typed logic with contexts given by sets of partial equations between the outcomes of actions. This provides a perspicuous and elegant treatment of reasoning about action, analogous to Reiter’s work on artificial intelligence. We define a sequent calculus for this logic, prove cut elimination, and give a semantics based...

Weak factorization systems, important in homotopy theory, are related to injective objects in comma{categories. Our main result is that full functors and topological functors form a weak factorization system in the category of small categories, and that this is not coobrantly generated. We also present a weak factorization system on the category of posets which is not coobrantly generated. No s...