Using Escardó-Flagg approach to injectivity via Kock-Zöberlein monads in T0 topological spaces [3], and Hofmann’s recent study of injectivity for spaces [4], we characterize continuous maps which are injective with respect to special classes of embeddings using convergence: see [1]. In fact, convergence has been shown to be very useful in the characterization of special classes of maps, like ef...

Abstract The equalizer of a set homomorphisms $S: F(a, b)\rightarrow F(\Delta)$ has rank at most two if S contains an injective map and is not finitely generated otherwise. This proves strong form Stallings’ Equalizer Conjecture for the free group two. Results are also obtained pairs $g, h:F(\Sigma)\rightarrow when images inert in, or retracts of, $F(\Delta)$.

Isbell and Semadeni [Trans. Amer. Math. Soc. 107 (1963)] proved that every infinite-dimensional $1$-injective Banach space contains a hyperplane is $(2+\varepsilon )$-injective for $\varepsilon \gt 0$, yet not $2$-injective, rem

We discuss various properties of a ring over which each simple module is Σ-injective. We shall consider associative rings with identity. Our modules will be unital right modules unless stated otherwise. The class of right V rings was introduced by Villamayor [20]. A ring R is called a right V ring if each simple right Rmodule is injective. It is a well-known unpublished result due to Kaplansky ...