ARTMAP with Modified Internal Category Geometry to Reduce the Category Proliferation

2012 ◽  
Keyword(s):  
Internal Category

Crossed Semimodules and Schreier Internal Categories in the Category of Monoids

1998 ◽  
Vol 5 (6) ◽  
pp. 575-581 ◽  
Author(s):  
A. Patchkoria
Keyword(s):  
Internal Category ◽  
Equivalence Of Categories ◽  
Crossed Modules

Abstract We introduce the notion of a Schreier internal category in the category of monoids and prove that the category of Schreier internal categories in the category of monoids is equivalent to the category of crossed semimodules. This extends a well-known equivalence of categories between the category of internal categories in the category of groups and the category of crossed modules.

scholarly journals Further remarks on group-2-groupoids

2021 ◽  
Vol 22 (1) ◽  
pp. 31
Author(s):  
Sedat Temel
Keyword(s):  
Special Kind ◽  
Internal Category ◽  
Crossed Modules ◽  
Group 2

The aim of this paper is to obtain a group-2-groupoid as a 2-groupoid object in the category of groups and also as a special kind of an internal category in the category of group-groupoids. Corresponding group-2-groupoids, we obtain some categorical structures related to crossed modules and group-groupoids and prove categorical equivalences between them. These results enable us to obtain 2-dimensional notions of group-groupoids.

A semiotic model for the description of levels in conjunction

1998 ◽  
Vol 5 (2) ◽  
pp. 179-211 ◽  
Author(s):  
Jean-Christophe Verstraete
Keyword(s):  
Main Clause ◽  
Comprehensive Model ◽  
Functional Grammar ◽  
Internal Category ◽  
Semiotic Model ◽  
Semantic Distinction

This paper attempts to develop a comprehensive model for the problem of internal vs. external conjunction (Halliday & Hasan 1976). It is first argued that the distinction between internal and external conjunction is not merely a matter of semantics, but that the two types are semiotically significant categories. By postulating that internal and external conjunction are cryptotypically anchored in the speaker-encoding vs. content-related grammar of their main clause, it can be explained why and how syntactic criteria like clefting or nominalization 'react' to the semantic distinction between the two types of conjunction. Secondly, it is argued that the internal category should be subdivided into two grammatically distinct types of conjunction, which are related to the modal and the speech functional grammar of their main clause. Finally, this analysis is used to propose a sharper delineation of the modal and the speech functional subtypes of the internal category.

Duplicity in possessive merger: evidence from Spanish alienable possessive constructions

2018 ◽  
Vol 35 (3) ◽  
pp. 371-412
Author(s):  
Sangyoon Kim
Keyword(s):  
Word Order ◽  
Relative Clauses ◽  
The Core ◽  
Internal Category ◽  
Direct Modification ◽  
Word Order Variation ◽  
Possessive Constructions ◽  
Order Variation ◽  
Principled Explanation

Abstract In this paper, I argue that Spanish prenominal and postnominal possessives target different external merge positions focusing on alienable possessive constructions. The analysis is developed alongside a proposal on the organization of DPs, according to which articles are merged as a DP-internal category between the domains assigned to direct and indirect modifiers. Prenominal possessives are determiners reanalyzed from direct modification adjectives whereas postnominal possessives are indirect modification adjectives that arise as predicates of reduced relative clauses. This analysis provides a principled explanation on the behavior of Spanish possessives that is lacking in the generalized idea that they are pronouns with a unique merge position. Arguments are also presented showing that syntax-driven phonological restrictions condition the derivation of DPs. The account successfully derives the core properties of word order variation and related issues within possessive constructions.

scholarly journals W-types in setoids

2021 ◽  
Vol Volume 17, Issue 3 ◽  
Author(s):  
Jacopo Emmenegger
Keyword(s):  
Type Theory ◽  
Internal Category ◽  
Initial Algebra

We present a construction of W-types in the setoid model of extensional Martin-L\"of type theory using dependent W-types in the underlying intensional theory. More precisely, we prove that the internal category of setoids has initial algebras for polynomial endofunctors. In particular, we characterise the setoid of algebra morphisms from the initial algebra to a given algebra as a setoid on a dependent W-type. We conclude by discussing the case of free setoids. We work in a fully intensional theory and, in fact, we assume identity types only when discussing free setoids. By using dependent W-types we can also avoid elimination into a type universe. The results have been verified in Coq and a formalisation is available on the author's GitHub page.

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