in this paper, we present algebroids and crossed modules of algebroids. we also define pullbackcrossed module of algebroids.

Valdis Laan in [5] introduced an extension of strong flatness which is called weak pullback flatness. In this paper we introduce a new property of acts over monoids, called U-WPF which is an extension of weak pullback flatness and give a classification of monoids by this property of their acts and also a classification of monoids when this property of acts implies others. We also show that regu...

A comprehensive account of the categorical properties category small categories and asymmetric delta lenses is given in recent works Chollet et al. Di Meglio. An important construction for proving many these Johnson Rosebrugh's "pullback" lenses, which we call proxy pullback lenses. We give a new treatment terms compatibility, stronger notion commutativity squares The sometimes, but not always,...

The representation of three-dimensional objects with point clouds is attracting increasing interest from researchers and practitioners. Since this requires a huge data volume, effective cloud compression techniques are required. One the most powerful solutions Moving Picture Experts Group geometry-based (G-PCC) emerging standard. In G-PCC lifting transform coding technique, an adaptive quantiza...

We call a finitely complete category diexact if every difunctional relation admits a pushout which is stable under pullback and itself a pullback. We prove three results relating to diexact categories: firstly, that a category is a pretopos if and only if it is diexact with a strict initial object; secondly, that a category is diexact if and only if it is Barr-exact, and every pair of monomorph...

Various Schlesinger transformations can be combined with a direct pull-back of a hypergeometric 2×2 system to obtainRS 4 -pullback transformations to isomonodromic 2× 2 Fuchsian systems with 4 singularities. The corresponding Painlevé VI solutions are algebraic functions, possibly in different orbits under Okamoto transformations. This paper demonstrates a direct computation of Schlesinger tran...

First, we introduce the concept of pullback ω-limit compactness for multivalued processes, as an extension of the similar concept in the autonomous and nonautonomous framework. Next, we present the necessary and sufficient conditions (pullback dissipativeness and pullback ω-limit compactness) for the existence of a nonempty local bounded kernel (kernel sections are all compact, invariant and pu...