The wide empirical coverage of two number features, [±singular] and [±augmented], is used to show that (Greenbergian) category-internal markedness, (geometric) feature markedness, and value markedness are, respectively, epiphenomenal, untenable, and too simplistically formulated to be currently evaluated.

We prove existence of equalizers in certain categories of cocomplete cocategories. This allows us to complete the proof of the fact that A∞-functor categories arise as internal Hom-objects in the category of differential graded cocomplete augmented cocategories.

In SGA 4 [1], one of the principal building blocks of the theory of topoi is Giraud’s theorem, which says that the condition of a 1-category A being the category of sheaves on a site, may be characterized by intrinsic, internal conditions in A. The intrinsic conditions are basically existence of certain limits and colimits, plus a condition about generation by a small set of objects. In this pa...

The original aim of this paper was to give a rather quick and undemanding proof that the effective topos contains two non-trivial small (i.e. internal) full subcategories which are closed under all small limits in the topos (and hence in particular are internally complete). The interest in such subcategories arises from the fact that they provide a very natural notion of model for many of the s...

We believe that the study of the notions of universal algebra modelled in an arbitarry topos rather than in the category of sets provides a deeper understanding of the real features of the algebraic notions. [2], [3], [4], [S], [6], [7], [13], [14] are some examples of this approach. The lattice Id(L) of ideals of a lattice L (in the category of sets) is an important ingredient of the categ...

Many perceptual categories exhibit internal structure in which category prototypes play an important role. In the four experiments reported here, the internal structure of phonetic categories was explored in studies involving adults, infants, and monkeys. In Experiment 1, adults rated the category goodness of 64 variants of the vowel i parallel on a scale from 1 to 7. The results showed that th...

The categorical definition of semidirect products was introduced by D. Bourn and G. Janelidze in [2], where they proved that, in the category of groups, this notion coincides with the classical one. A characterization of pointed categories with categorical semidirect products was given in [3]. The existence of such products imply, in particular, that the category is protomodular, i.e. the Split...

We present a cubical type theory based on the Cartesian cube category (faces, degeneracies, symmetries, diagonals, but no connections or reversal) with univalent universes, each containing Π, Σ, path, identity, natural number, boolean, pushout, and glue (equivalence extension) types. The type theory includes a syntactic description of a uniform Kan operation, along with judgemental equality rul...