We combine two research directions of the past decade, namely the development of a lax-algebraic framework for categories of interest to topologists and analysts, and the exploration of key topological concepts, like separation and compactness, in an abstract category which comes equipped with an axiomatic notion “closed” or “proper” map. Hence, we present various candidates for such notions in...

The generation effect has been central to theoretical analyses of implicit memory and has been used as a criterion for classifying implicit tests as conceptual. The present experiments demonstrate that generation does not always enhance conceptual implicit memory. Four experiments examined the effects of generation on conceptual implicit and explicit memory in category-exemplar production and c...

So-called ∗-autonomous, or “Frobenius”, category structures occur widely in mathematical quantum theory. This trend was observed in [3], mainly in relation to Hopf algebroids, and continued in [8] with a general account of Frobenius monoids. Below we list some of the ∗-autonomous partially ordered sets A = (A , p, j, S) that appear in the literature, an abstract definition of ∗-autonomous promo...

We characterize the finite EI categories whose representations are standardly stratified with respect to the natural preorder on the simple representations. The orbit category of a finite group with respect to any set of subgroups is always such a category. Taking the subgroups to be the p-subgroups of the group, we reformulate Alperin’s weight conjecture in terms of the standard and proper cos...

Given a map f in the category ω-Cpo of ω-complete posets, exponentiability of f in ω-Cpo easily implies exponentiability of f in the category Pos of posets, while the converse is not true. We find then the extra conditions needed on f exponentiable in Pos to be exponentiable in ω-Cpo, showing the existence of partial products of the two-point ordered set S = {0 < 1} (Theorem 1.8). Using this ch...

We investigate the behaviour of split extensions in category $OrdGrp$ (pre)- ordered groups. Namely we show that lexicographic order plays a key role on existence compatible orders for semidirect products, establishing necessary and sufficient conditions such existence; prove Split Short Five Lemma holds (stably) strong extensions, identify classes which admit classifier.

The stereotype regression model for categorical outcomes, proposed by Anderson (J. Roy. Statist. Soc. B. 1984; 46:1-30) is nested between the baseline-category logits and adjacent category logits model with proportional odds structure. The stereotype model is more parsimonious than the ordinary baseline-category (or multinomial logistic) model due to a product representation of the log-odds-rat...

Abstract We overview the notion of entropy in thermodynamics. start from smooth case using differential forms on manifold, which is natural language for Then axiomatic definition as ordering a set that induced by adiabatic processes will be outlined. Finally, viewpoint category theory provided, reinterprets structure pre-ordered sets.