A partial generalization of a theorem of Hursch
For categories with equalizers the concepts ``accessible'' and ``axiomatizable'' are equivalent. This results is proved under (in fact, is equivalent to) the large-cardinal Vopěnka's principle.
We extend a result of M. M. Kapranov and Y. Manin concerning the Morita theory for linear operads. We also give a cyclic operad version of their result.
Let R be an associative ring with 1 and R-tors the somplete Brouwerian lattice of all hereditary torsion theories on the category of left R-modules. A well known result asserts that R is a left semiartinian ring iff R-tors is a complete atomic Boolean lattice. In this note we prove that if L is a complete atomic Boolean lattice then there exists a left semiartinian ring R such that L is lattice-isomorphic to R-tors.