Aristotle's Categories can easily seem to be a statement of a naïve, pre- philosophical ontology, centered around ordinary items. Wolfgang-Rainer Mann argues that the treatise, in fact, presents a ...revolutionary metaphysical picture, one Aristotle arrives at by (implicitly) criticizing Plato and Plato's strange counterparts, the "Late-Learners" of the Sophist. As Mann shows, the Categories reflects Aristotle's discovery that ordinary items are things (objects with properties). Put most starkly, Mann contends that there were no things before Aristotle. The author's argument consists of two main elements. First, a careful investigation of Plato which aims to make sense of the odd-sounding suggestion that things do not show up as things in his ontology. Secondly, an exposition of the theoretical apparatus Aristotle introduces in the Categories --an exposition which shows how Plato's and the Late-Learners' metaphysical pictures cannot help but seem inadequate in light of that apparatus. In doing so, Mann reveals that Aristotle's conception of things--now so engrained in Western thought as to seem a natural expression of common sense--was really a hard-won philosophical achievement. Clear, subtle, and rigorously argued, The Discovery of Things will reshape our understanding of some of Aristotle's--and Plato's--most basic ideas.
Emotional illiteracy exists in current e-learning environment, which will decay learning enthusiasm and productivity, and now gets more attentions in recent researches. Inspired by affective ...computing and active listening strategy, in this paper, a research and application framework of recognizing emotion based on textual interaction is presented first. Second, an emotion category model for e-learners is defined. Third, many Chinese metaphors are abstracted from the corpus according to the sentence semantics and syntax. Fourth, as the strategy of active learning, topic detection is used to detect the first turn in dialogs and recognize the type of emotion in the turn, which is different from the traditional emotion recognition approaches that try to classify every turn into an emotion category. Fifth, compared with Support Vector Machines (SVM), Naive Bayes, LogitBoost, Bagging, MultiClass Classifier, RBFnetwork, J48 algorithms and their corresponding cost-sensitive approaches, Random Forest and its corresponding cost-sensitive approaches achieve better results in our initial experiment of classifying the e-learnersa emotions. Finally, a case-based reasoning for emotion regulation instance recommendation is proposed to guide the listener to regulate the negative emotion of a speaker, in which a weighted sum method of Chinese sentence similarity computation is adopted. The experimental result shows that the ratio of effective cases is 68%.
In this article, we show that the localization of an extriangulated category by a multiplicative system satisfying mild assumptions can be equipped with a natural, universal structure of an ...extriangulated category. This construction unifies the Serre quotient of abelian categories and the Verdier quotient of triangulated categories. Indeed we give such a construction for a bit wider class of morphisms, so that it covers several other localizations appeared in the literature, such as Rump's localization of exact categories by biresolving subcategories, localizations of extriangulated categories by means of Hovey twin cotorsion pairs, and the localization of exact categories by two-sided admissibly percolating subcategories.
We investigate several homological aspects of recollements of abelian categories. In particular, we study how various homological invariants and dimensions of the categories involved in a recollement ...situation are related, and when recollements of abelian categories induce recollements at the level of the bounded derived categories. Finally we give applications to global, finitistic, and representation dimension of rings and Artin algebras, and to Rouquierʼs dimension of triangulated categories.
Additive categories play a fundamental role in mathematics and related disciplines. Given an additive category equipped with a biadditive functor, one can construct its category of extensions, which ...encodes important structural information. We study how functors between categories of extensions relate to those at the level of the original categories. When the additive categories in question are
n
-exangulated, this leads to a characterisation of
n
-exangulated functors. Our approach enables us to study
n
-exangulated categories from a 2-categorical perspective. We introduce
n
-exangulated natural transformations and characterise them using categories of extensions. Our characterisations allow us to establish a 2-functor between the 2-categories of small
n
-exangulated categories and small exact categories. A similar result with no smallness assumption is also proved. We employ our theory to produce various examples of
n
-exangulated functors and natural transformations. Although the motivation for this article stems from representation theory and the study of
n
-exangulated categories, our results are widely applicable: several require only an additive category equipped with a biadditive functor with no extra assumptions; others can be applied by endowing an additive category with its split
n
-exangulated structure.
In this article, we introduce the notion of a pre-(n+2)-angulated category as a higher dimensional analogue of a pre-triangulated category defined by Beligiannis-Reiten. We first show that the ...idempotent completion of a pre-(n+2)-angulated category admits a unique pre-(n+2)-angulated structure. Let (C,E,s) be an n-exangulated category and X be a strongly functorially finite subcategory of C. We then show that the quotient category C/X is a pre-(n+2)-angulated category. These results allow to construct several examples of pre-(n+2)-angulated categories. Moreover, we also give a necessary and sufficient condition for the quotient C/X to be an (n+2)-angulated category.
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