Both intention-based and causation-based definitions of the miraculous make reference to the term ‘supernatural’. Philosophers who define the miraculous appear to use this term in a loose way, perhaps meaning the nonnatural, perhaps meaning a subcategory of the nonnatural. Here I examine the aetiology of the term ‘supernatural’. I consider three outstanding issues regarding the meaning of the t...

The role and limitations of retrospective investigations of factors possibly associated with the occurrence of a disease are discussed and their relationship to forward-type studies emphasized. Examples of situations in which misleading associations could arise through the use of inappropriate control groups are presented. The possibility of misleading associations may be minimized by controlli...

We construct a functor from the derived category of homotopy Gerstenhaber algebras, g, with finite-dimensional cohomology to the purely geometric category of so-called F ∞-manifolds. The latter contains Frobenius manifolds as a subcategory (so that a pointed Frobenius manifold is itself a homotopy Gerstenhaber algebra). If g happens to be formal as a L ∞-algebra, then its F ∞-manifold comes equ...

Background in history of music. In music history it is often considered important to have a reliable overview of the oeuvre of a certain composer. Unfortunately many pieces exist of which the composer cannot be determined with great certainty. Not rarely this leads to authorship-discussions. Various kinds of evidence are used to defend an attribution. These can be categorized into external and ...

Let R be an associative ring with non-zero identity. For a Serre subcategory C of the category R-mod of left R-modules, we consider the class AC of all modules that do not belong to C, but all of their proper submodules belong to C. Alongside of basic properties of such associated classes of modules, we will prove that every uniform module of AC has a local endomorphism ring. Moreover, if R is ...

there are different views, about the authenticity of esteshal (masalehe morsalah), among the religious jurisprudences of sunnite and emamieh. each of them has offered arguments possibly in rejecting and proving esteslah, but they took an extreme in their arguments. the present study attempts to prove that esteslah, which had been presented by jurisprudents, in the context of social issues, is d...

We show that if C is the category of models for a theory in the sense of Linton over an arbitrary base category, then a full subcategory of C is closed under Homomorphic images that split in the underlying category, under M -Subobjects for a class M of monomorphisms and under Products if and only if it is an intersection of a nest of subcategories, each determined from the preceding by a class ...

A C∞-Hopf algebra is a C∞-algebra which is also a convenient Hopf algebra with respect to the structure induced by the evaluations of smooth functions. We characterize those C∞-Hopf algebras which are given by the algebra C∞(G) of smooth functions on some compact Lie group G, thus obtaining an anti-isomorphism of the category of compact Lie groups with a subcategory of convenient Hopf algebras.

Let P be an abelian p-group, E a cyclic p′-group acting freely on P and k an algebraically closed field of characteristic p > 0. In this work, we prove that every self-equivalence of the stable module category of k[P oE] comes from a self-equivalence of the derived category of k[P o E]. Work of Puig and Rickard allows us to deduce that if a block B with defect group P and inertial quotient E is...