There are three equivalent definitions of dimension for partially ordered sets. When generating these three definitions to ~'-dimension over an arbitrary class of orders ~, the three definitions diverge. We compare these three definitions and determine certain requirements under which they are equivalent.

The category of Hopf monoids over an arbitrary symmetric monoidal category as well as its subcategories of commutative and cocommutative objects respectively are studied, where attention is paid in particular to the following questions: (a) When are the canonical forgetful functors of these categories into the categories of monoids and comonoids respectively part of an adjunction? (b) When are ...

Patients with Parkinson disease often have orthostatic hypotension. Neurocirculatory abnormalities underlying orthostatic hypotension might reflect levodopa treatment. Sixty-six Parkinson disease patients (36 with orthostatic hypotension, 15 off and 21 on levodopa; 30 without orthostatic hypotension) had tests of reflexive cardiovagal gain (decrease in interbeat interval per unit decrease in sy...

A wealth of data indicate that central spatially nonpredictive eyes and arrows trigger very similar reflexive spatial orienting, although the effects of eyes may be more strongly reflexive (e.g., Friesen, Ristic, & Kingstone, 2004). Pratt and Hommel (2003) recently reported that the orienting effect for arrows is sensitive to arbitrary cue-target color contingencies; for example, an attentional...

We propose a concept of module liaison that extends Gorenstein liaison of ideals and provides an equivalence relation among unmixed modules over a commutative Gorenstein ring. Analyzing the resulting equivalence classes we show that several results known for Gorenstein liaison are still true in the more general case of module liaison. In particular, we construct two maps from the set of even li...

Canonical orders, introduced in the minimal model program for orders [CI05], are simultaneous generalisations of Kleinian singularities k[[s, t]], G < SL2 and their associated skew group rings k[[s, t]]∗G. In this paper, we construct minimal resolutions of canonical orders via non-commutative cyclic covers and skew group rings. This allows us to exhibit a derived equivalence between minimal res...

The theory of protomodular categories provides a simple and general context in which the basic theorems needed in homological algebra of groups, rings, Lie algebras and other non-abelian structures can be proved [2] [3] [4] [5] [6] [7] [9] [20]. An interesting aspect of the theory comes from the fact that there is a natural intrinsic notion of normal monomorphism [4]. Since any internal reflexi...