‎We firstly prove the completeness of the category of crossed modules in a modified category of interest‎. ‎Afterwards‎, ‎we define pullback crossed modules and pullback cat objects that are both obtained by pullback diagrams with extra structures on certain arrows‎. ‎These constructions unify many corresponding results for the cases of groups‎, ‎commutative algebras and can also be adapted to ...

At present paper, we establish the existence of pullback $mathcal{D}$-attractor for the process associated with non-autonomous partly dissipative reaction-diffusion equation in $L^2(mathbb{R}^n)times L^2(mathbb{R}^n)$. In order to do this, by energy equation method we show that the process, which possesses a pullback $mathcal{D}$-absorbing set, is pullback $widehat{D}_0$-asymptotically compact.

OBJECTIVE To observe the intracochlear behavior of a cochlear implant electrode insertion technique (called "pullback") in temporal bones. Study Design. Experimental. Settings. Tertiary referral center. METHOD The change of the intracochlear electrode position was investigated under various conditions of an electrode pullback (N = 54) in 9 radiologically, size-estimated temporal bones (TBs). ...

at present paper, we establish the existence of pullback $mathcal{d}$-attractor for the process associated with non-autonomous partly dissipative reaction-diffusion equation in $l^2(mathbb{r}^n)times l^2(mathbb{r}^n)$. in order to do this, by energy equation method we show that the process, which possesses a pullback $mathcal{d}$-absorbing set, is pullback $widehat{d}_0$-asymptotically compact.

Introduction: Endovenous laser treatment (ELT) is a new treatment method for the reflux of the great saphenous vein. A successful ELT is dependent on the selection of optimum parameters required to achieve optimal vein damage while avoiding side effects including skin burns. The mathematical modeling of ELT can be used to understand the process of ELT. This study was conducted to examine the ef...

In this paper‎, ‎we give the notions of crossed polymodule and cat$^1$-polygroup‎ ‎as a generalization of Loday's definition‎. ‎Then‎, ‎we define the pullback cat$^1$-polygroup and we obtain some results in this respect‎. ‎Specially‎, ‎we prove that by a pullback cat$^1$-polygroup we can obtain a cat$^1$-group‎.

The notion of pullback rewriting has been developed recently as a category theoretical framework for vertex replacement in graphs. Here, the technique is presented based on net morphisms, yielding a well-deened mechanism which is closely related to pullback rewriting in hypergraphs. Finally, a net reenement operation modifying the context of the reened transition is characterized in terms of pu...

The main purpose of this article is to introduce the categorical concept of pullback in Mizar. In the first part of this article we redefine homsets, monomorphisms, epimorpshisms and isomorphisms [6] within a free-object category [15] and it is shown there that ordinal numbers can be considered as categories. Then the pullback is introduced in terms of its universal property, and the Pullback L...

in this paper‎, ‎we give the notions of crossed polymodule and cat$^1$-polygroup‎ ‎as a generalization of loday's definition‎. ‎then‎, ‎we define the pullback cat$^1$-polygroup and we obtain some results in this respect‎. ‎specially‎, ‎we prove that by a pullback cat$^1$-polygroup we can obtain a cat$^1$-group‎.