‎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 ...

We classify the paracontact Riemannian manifolds that their Riemannian curvature satisfies in the certain condition and we show that this classification is hold for the special cases semi-symmetric and locally symmetric spaces. Finally we study paracontact Riemannian manifolds satisfying R(X, ξ).S = 0, where S is the Ricci tensor.

The association of granuloma annulare and some neoplasms is controversial. However, there is an increase in the number of case reports and relevant studies supporting the conceptof granuloma annulare being associated with certain types of hematologic neoplasms and solid tumors.Herein, we describe a 54-year-old woman with a 20-month history of generalized annular lesions that did not respond to ...