We introduce a very general extension of the monomorphism category as studied by Ringel and Schmidmeier which in particular covers generalised species over locally bounded quivers. prove that analogues kernel cokernel functor send almost split sequences path algebra preprojective to or category. derive this from result on preservation morphisms under adjoint functors whose counit is monomorphis...

Let S be a d-dimensional separoid of (k− 1)(d+1)+1 convex sets in some ‘large-dimensional’ Euclidean space IE . We prove a theorem that can be interpreted as follows: if the separoid S can be mapped with a monomorphism to a d-dimensional separoid of points P in general position, then there exists a k-colouring ς:S → Kk such that, for each pair of colours i, j ∈ Kk, the convex hulls of their pre...

Suppose that M is a connected orientable n-dimensional manifold and m > 2n. If H(M, R) = 0 for i > 0, it is proved that for each m there is a monomorphism Hm(Wn, O(n)) → H m cont(Diff M, R). If M is closed and oriented, it is proved that for each m there is a monomorphism Hm(Wn, O(n)) → H m−n cont (Diff+ M, R), where Diff+ M is the group of orientation preserving diffeomorphisms of M . 2000 Mat...

In this paper, in addition to some elementary facts about the ultra-groups, which their structure based on the properties of the transversal of a subgroup of a group, we focus on the relation between a group and an ultra-group. It is verified that every group is an ultra-group, but the converse is not true generally. We present the conditions under which, for every normal subultra-group of an u...

Let be a commutative ring with 1 and left unitary . In this papers we introduced studied concept P-small compressible (An is said to if can embedded in every of it nonzero submodule Equivalently, there exists monomorphism , retractable for non-zero homomorphism whenever as generalization respectively give some their advantages characterizations examples.

‎In this paper we take $mathcal A$ to be the category {bf Pos-S}‎ ‎of $S$-posets‎, ‎for a posemigroup $S$‎, ${mathcal M}_{pd}$ to‎ ‎be the class of partially ordered sequantially-dense‎ ‎monomorphisms and study the categorical properties‎, ‎such as‎ ‎limits and colimits‎, ‎of this class‎. ‎These properties are usually‎ ‎needed to study the homological notions‎, ‎such as injectivity‎, ‎of‎ ‎$S$-...