A∞-method in Lusternik–Schnirelmann category

Injectivity in a category: an overview on smallness conditions

Some of the so called smallness conditions in algebra as well as in category theory, are important and interesting for their own and also tightly related to injectivity, are essential boundedness, cogenerating set, and residual smallness. In this overview paper, we first try to refresh these smallness condition by giving the detailed proofs of the results mainly by Bernhard Banaschewski and W...

Axiomatic Method and Category Theory

The category of monoid actions in Cpo

In this paper, some categorical properties of the category ${bf Cpo}_{{bf Act}text{-}S}$ of all {cpo $S$-acts}, cpo's equipped with actions of a monoid $S$ on them, and strict continuous action-preserving maps between them is considered. In particular, we describe products and coproducts in this category, and consider monomorphisms and epimorphisms. Also, we show that the forgetful functor from...

A Category Resolve Power-Based Feature Selection Method

One of the most important issues in Text Categorization (TC) is Feature Selection (FS). Many FS methods have been put forward and widely used in TC field, such as Information Gain (IG), Document Frequency (DF) thresholding, Mutual Information (MI) and so on. Empirical studies show that IG is one of the most effective methods, DF performs similarly, in contrast, and MI had relatively poor perfor...

A category-dependent feature selection method for speech signals

We present a novel method of dimension reduction and feature selection that makes use of category-dependent regions in high-dimensional data. Our method is inspired by phonemedependent, noise-robust low-variance regions observed in the cortical response, and introduces the notion of categorydependence in a two-step dimension reduction process that draws on the fundamental principles of Fisher L...