a toroidalization of a dominant morphism $varphi: xto y$ of algebraic varieties over a field of characteristic zero is a toroidal lifting of $varphi$ obtained by performing sequences of blow ups of nonsingular subvarieties above $x$ and $y$. we give a proof of toroidalization of locally toroidal morphisms of 3-folds.

The concept of a coset-preserving skew-morphism is a generalization of the widely studied t-balanced skew-morphisms of regular Cayley maps which are in turn generalizations of group automorphisms. In case of abelian groups, all skew-morphisms of regular Cayley maps are roots of coset-preserving skew-morphisms, and therefore, classification of cosetpreserving skew-morphisms of finite abelian gro...

Deleanu, Frei, and Hilton have developed the notion of generalized Adams completion in a categorical context. In this paper, we have obtained the Postnikov-like approximation of a module, with the help of a suitable set of morphisms.

‎In this paper‎, ‎we prove that the category of crossed polymodules (i.e‎. ‎crossed modules of polygroups) and their morphisms is finitely complete‎. ‎We‎, ‎therefore‎, ‎generalize the group theoretical case of this completeness property of crossed modules‎.

[A] M. Svensson, On holomorphic harmonic morphisms, Manuscripta Math. 107 (2002), 1–13. [B] M. Svensson, Harmonic morphisms from even-dimensional hyperbolic spaces, Math. Scand. 92 (2003), 246–260. [C] M. Svensson, Holomorphic foliations, harmonic morphisms and the Walczak formula, J. London Math. Soc. 68 (2003), 781–794. [D] M. Svensson, Harmonic morphisms in Hermitian geometry, J. Reine Angew...

Local deterministic string-to-string transductions are generalizations of morphisms on free monoids. Learning local transductions reduces to inference of monoid morphisms. However, learning a restricted class of morphisms, the so-called fine morphisms, is an intractable problem, because the decision version of the empirical risk minimization problem contains an NP-complete subproblem.

In the present paper, we introduce bounded morphisms on bi-approximation semantics, show the so-called p-morphism lemma on bi-approximation semantics, and investigate the dual representation of the morphisms. In addition, we study three properties, namely B-embedding, B-separating and B-reflecting, to preserve validity of sequents on frames. These bounded morphisms do not look like embedding, s...