We set up a fibred categorical theory of obstruction and classification morphisms that specialises to the one monoidal functors between groups also Schreier-Mac Lane group extensions. Further applications are provided crossed extensions bimodule butterflies, with in particular non-abelian unital associative algebras terms Hochschild cohomology.

Inclusion diagrams are introduced as an alternative to using Venn diagrams to determine the validity of categorical syllogisms, and are used here for the analysis of diverse categorical syllogisms. As a preliminary example of a possible generalization of the use of inclusion diagrams, consideration is given also to an argument that includes more than two premises and more than three terms, the ...

Analyzing multivariate datasets requires users to understand distributions of single variables and at least the two-way relationships between the variables. Lower-dimension projection techniques may assist users in finding interesting combinations. To explore the 2D relationships in a systematic way, we suggest ranking such relationships according to some measure of interestingness. This approa...

Through random cut-points theory, the author extends inference for ordered categorical data to the unspecified continuum underlying the ordered categories. He shows that a random cut-point Mann–Whitney test yields slightly smaller p-values than the conventional test for most data. However, when at least P% of the data lie in one of the k categories (with P = 80 for k = 2, P = 67 for k = 3, . . ...

Categorical data appears in various places, and dealing with it has been a major concern in analysis fields. However, representing not only global trends but also local trends of data simultaneously by conventional techniques is difficult. We propose a visualization method called “granular representation” for analyzing categorical data visually. Our approach visually represents data as a set of...