In this article we study injective representations of infinite quivers. We classify the indecomposable injective representations of trees and then describe Gorenstein injective and projective representations of barren trees.

We give some new properties of almost injective modules and their endomorphism rings, and also provide conditions as to when a direct sum of almost injective (or CS) modules is again almost injective (or CS) in some special cases..

Linking diagrams with path composition are ubiquitous, for example: Temperley-Lieb and Brauer monoids, Kelly-Laplaza graphs for compact closed categories, and Girard’s multiplicative proof nets. We construct the category Link = Span(iRel), where iRel is the category of injective relations (reversed partial functions) and show that the aforementioned linkings, as well as Jones-Martin partition m...

Let A be a special biserial algebra over an algebraically closed field. We show that the first Hohchshild cohomology group of A with coefficients in the bimodule A vanishes if and only if A is representation finite and simply connected (in the sense of Bongartz and Gabriel), if and only if the Euler characteristic of Q equals the number of indecomposable non uniserial projective injective A-mod...

In this paper, we consider high-level structures like graphs, Petri nets, and algebraic specifications and investigate two kinds of satisfiability of conditions and two kinds of rule matching over these structures. We show that, for weak adhesive HLR categories with class A of all morphisms and a class M of monomorphisms, strictly closed under decompositions, Aand M-satisfiability and Aand M-ma...

Two 4-manifolds are stably diffeomorphic if they become diffeomorphic after connected sum with S × S’s. This paper shows that two closed, orientable, homotopy equivalent, smooth 4-manifolds are stably diffeomorphic provided a certain map from the second homology of the fundamental group with coefficients in Z2 to the L-theory of the group is injective. This injectivity is implied by the Borel/N...

We reconstruct Milner’s [1] category of abstract binding bigraphs Bbg(K) over a signature K as the free (or initial) symmetric monoidal closed (smc) category S(TK) generated by a derived theory TK. The morphisms of S(TK) are essentially proof nets from the Intuitionistic Multiplicative fragment (imll) of Linear Logic [2]. Formally, we construct a faithful, essentially injective on objects funct...

Marden and Strebel established the Heights Theorem for integrable holomorphic quadratic differentials on parabolic Riemann surfaces. We extends validity of to all surfaces whose fundamental group is first kind. In fact, we establish a more general result: horizontal map which assigns each differential measured lamination obtained by straightening trajectories injective an arbitrary surface with...

In act theory, Pseudo injective acts and their generalizations are essential. As a result, the purpose of this work is to give generalization pseudo quasi principally specifically small acts. Besides, concept was presented, which can be employed later. If each S-monomorphism from M-cyclic sub-act M\textsubscript{S} N\textsubscript{S} extended S-homomorphism N\textsubscript{S}, An S-act called p...