On some adjunctions between the categories of adjunction-morphisms and monad-morphisms

Free Adjunction of Morphisms

We develop a general setting for the treatment of extensions of categories by means of freely adjoined morphisms. To this end, we study what we call composition graphs, i.e. large graphs with a partial binary operation on which we impose only rudimentary requirements. The quasicategory thus obtained contains the quasicategory of all categories as a full reflective subquasicategory; we character...

Some remarks on morphisms between Fano threefolds

Some twenty-five years ago, Iskovskih classified the smooth complex Fano threefolds with Picard number one. Apart from P and the quadric, his list includes 5 families of Fano varieties of index two and 11 families of varieties of index one (for index one threefolds, the cube of the anticanonical divisor takes all even values from 2 to 22, except 20). Recently, the author ([A]) and C. Schuhmann ...

Graph Rewriting in Some Categories of Partial Morphisms

We present a definition of term graph rewriting as the taking of a pushout in a category of partial morphisms, adapting the rather ad hoc definitions we gave in [Ken87] so as to use a standard category-theoretic concept of partial morphism. This single-pushout construction is shown to coincide with the well-known double-pushout description of graph rewriting whenever the latter is defined. In g...

On morphisms of crossed polymodules

‎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.

Partial Morphisms in Categories of Effective Objects