On three types of simplicial objects
On torsionfree classes which are not precover classes
In the class of all exact torsion theories the torsionfree classes are cover (precover) classes if and only if the classes of torsionfree relatively injective modules or relatively exact modules are cover (precover) classes, and this happens exactly if and only if the torsion theory is of finite type. Using the transfinite induction in the second half of the paper a new construction of a torsionfree relatively injective cover of an arbitrary module with respect to Goldie’s torsion theory of finite...
On triangulated orbit categories.
One-sided -suspended categories
For an integer , we introduce a simultaneous generalization of -exact categories and -angulated categories, referred to as one-sided -suspended categories. Notably, one-sided -angulated categories are specific instances of this structure. We establish a framework for transitioning from these generalized categories to their -angulated counterparts. Additionally, we present a method for constructing -angulated quotient categories from Frobenius -prile categories. Our results unify and extend...