We treat a relative version of the main theorem in [F2]: A transcendental approach to Kollár’s injectivity theorem. More explicitly, we give a curvature condition that implies Kollár type cohomology injectivity theorems in the relative setting. To carry out this generalization, we use Ohsawa-Takegoshi’s twisted version of Nakano’s identity.

In a locally λ-presentable category, with λ a regular cardinal, classes of objects that are injective with respect to a family of morphisms whose domains and codomains are λ-presentable, are known to be characterized by their closure under products, λ-directed colimits and λ-pure subobjects. Replacing the strict commutativity of diagrams by “commutativity up to ε”, this paper provides an “appro...

‎for the subclasses ${mathcal m}_1$ and ${mathcal m}_2$ of‎‎monomorphisms in a concrete category $mathcal c$‎, ‎if ${mathcal‎‎m}_2subseteq {mathcal m}_1$‎, ‎then ${mathcal m}_1$-injectivity‎‎implies ${mathcal m}_2$-injectivity‎. ‎the baer type criterion is about‎ ‎the converse of this fact‎. ‎in this paper‎, ‎we apply injectivity to the classes of {it $c$-dense‎, ‎$c$-closed}‎ ‎monomorphisms‎. ...

Suppose we are given a pseudo-linearly convex triangle F . In [30], the main result was the construction of totally universal triangles. We show that S (π, ι̃) ∼ { 1 ‖Ī‖ : √ 2 −4 = ⋂ X ( R′ )}

Abstract We investigate the injective types and algebraically in univalent mathematics, both absence presence of propositional resizing. Injectivity is defined by surjectivity restriction map along any embedding, algebraic injectivity a given section embedding. Under resizing axioms, main results are easy to state: (1) equivalent truncation injectivity. (2) The precisely retracts exponential po...

We develop a rigorous algebraic background for representations of triangle groups in linear groups over algebras arising from factor rings of multivariate polynomial rings. This is then used to substantially improve the existing upper bounds on the order of epimorphic images of triangle groups with a given injectivity radius and, analogously, the size of the associated hypermaps of a given type...

Abstract. We show that the Strong Novikov Conjecture for the maximal C∗-algebra C∗(π) of a discrete group π is equivalent to a statement in topological K-theory for which the corresponding statement in algebraic K-theory is always true. We also show that for any group π , rational injectivity of the full assembly map for K ∗(C ∗(π)) follows from rational injectivity of the restricted assembly map.