We describe a certain category of Ind-towers into which the Pro category of towers of simplicial sets embeds, and in which all colimits (rather than just the finite ones) may be constructed explicitly.

Models undergo a variety of transformations throughout development. One of the key transformations is merge, used when developers need to combine a set of models with respect to the overlaps between them. A major question about model transformations in general, and merge in particular, is what consistency properties are preserved across the transformations and what consistency properties may ne...

Category theory can be applied to mathematically model the semantics of cognitive neural systems. Here, we employ colimits, functors and natural transformations to model the implementation of concept hierarchies in neural networks equipped with multiple sensors.

We study cocompleteness, co-wellpoweredness, and generators in the centralizer category of an object or morphism a monoidal category, center weak category. explicitly give some answers for when colimits, these categories can be inherited from their base monidal categories. Most importantly, we investigate cofree objects comonoids

The goal of this paper is to demystify the role played by the Reedy category axioms in homotopy theory. With no assumed prerequisites beyond a healthy appetite for category theoretic arguments, we present streamlined proofs of a number of useful technical results, which are well known to folklore but di cult to nd in the literature. While the results presented here are not new, our approach to ...

Algebra transformation systems are introduced as formal models of components of open distributed systems. They are given by a transition graph modelling the control ow and partial algebras and method expressions modelling the data states and their transformations. According to this two{level structure they cover both labelled transition systems and rule based speciication approaches, correspond...

let $s$ be a monoid. in this paper, we prove every class of $s$-acts having a flatness property is closed underdirected colimits, it extends some known results. furthermore thisresult implies that every $s$-act has a flatness cover if and only if it has a flatness precover.