We consider the equivalence of Lawvere theories and finitary monads on Set from the perspective of Endf (Set)-enriched category theory, where Endf (Set) is the category of finitary endofunctors of Set. We identify finitary monads with one-object Endf (Set)-categories, and ordinary categories admitting finite powers (i.e., n-fold products of each object with itself) with Endf (Set)-categories ad...

Ordered sheaves on a small quantaloid Q have been defined in terms of Q-enriched categorical structures; they form a locally ordered category Ord(Q). It has previously been shown by the second author that the " free-cocompletion " KZ-doctrine on Ord(Q) has Mod(Q), the quantaloid of Q-modules, as category of Eilenberg-Moore algebras. In the first part of this paper we apply Q-enriched category t...

The finite π-calculus has an explicit set-theoretic functor-category model that is known to be fully abstract for strong late bisimulation congruence. We characterize this as the initial free algebra for an appropriate set of operations and equations in the enriched Lawvere theories of Plotkin and Power. Thus we obtain a novel algebraic description for models of the π-calculus, and validate an ...

The study of multi-agent systems is proving to be an exciting and active research field within computer science. Communication is an important aspect of multi-agent systems, and the protocols that are used to provide a shared definition of what agents can say to each other, along with the meaning of what agents say, receive much attention from researchers. At present, there are a number of well...

We introduce the notion of weighted limit in an arbitrary quasi-category, suitably generalizing ordinary limits a and classical category. This is accomplished by Joyal’s approach: we identify meaningful construction for quasi-category cones over diagram whose terminal object considered diagram. then show that each can be expressed as limit. When arises homotopy coherent nerve category enriched ...

Our work over the past years shows that not only the collection of (for instance) all topological spaces gives rise to a category, but also each topological space can be seen individually as a category by interpreting the convergence relation x −→ x between ultrafilters and points of a topological space X as arrows in X. Naturally, this point of view opens the door to the use of concepts and id...

The ultimate purpose of this part is to explain the definition of models for the rational homotopy of spaces. In our constructions, we use the classical Sullivan model, defined in terms of unitary commutative cochain dg-algebras, and a cosimplicial version of this model, involving cosimplicial algebra structures. The purpose of this preliminary chapter is to provide a survey of constructions on...

We introduce, comment and develop the Scott adjunction, mostly from point of view a category theorist. Besides its technical conceptual aspects, in nutshell we provide categorification topology over posets with directed suprema. From establish an adjunction between accessible categories colimits Grothendieck topoi. show that bicategory topoi is enriched $2$-category it has tensors respect to th...

In this paper, we study linear rewriting systems modulo a set of algebraic axioms. We introduce the structure (3,2)-polygraph as presentation category enriched in categories, (called (2,2)-category), by system symbolic computation method order to compute bases for vector spaces 2-cells these categories. particular, case pivotal 2-categories using isotopy relations given biadjunctions on 1-cells...

Homotopy limits and colimits are homotopical replacements for the usual limits and colimits of category theory, which can be approached either using classical explicit constructions or the modern abstract machinery of derived functors. Our first goal is to explain both and show their equivalence. Our second goal is to generalize this result to enriched categories and homotopy weighted limits, s...