When replacing the non-negative real numbers with their addition by a commutative quantale V, under a metric lens one may then view small V-categories as sets that come with a V-valued distance function. The ensuing category V-Cat is well known to be a concrete topological category that is symmetric monoidal closed. In this paper we show which concrete symmetric monoidalclosed topological categ...

In this article we study the problem of extracting an ∞-category from a relative category. We introduce partial model categories, which are relative categories that satisfy mild versions of the axioms of a model category. Since these axioms involve only the weak equivalences, they are general enough to include the vast majority of the relative categories one encounters in practice. We show that...

An additive category is definable if it is equivalent to a definable subcategory of a module category Mod-R, meaning a full subcategory which is closed under direct products, direct limits (= directed colimits) and pure subobjects. Such a category D has associated to it a canonical model theory for its objects in the sense that each object D ∈ D becomes a structure for the associated language; ...

Recall that for a triangulated category T , a Bousfield localization is an exact functor L : T → T which is coaugmented (there is a natural transformation Id → L; sometimes L is referred to as a pointed endofunctor) and idempotent (there is a natural isomorphism Lη = ηL : L → LL). The kernel ker(L) is the collection of objects X such that LX = 0. If T is closed under coproducts, it’s a localizi...

This is a longitudinal case study of two Farsi-speaking children learning English: ‘Bernard’ and ‘Melissa’, who were 7;4 and 8;4 at the start of data collection. The research deals with the initial state and further development in the child second language (L2) acquisition of syntax regarding the presence or absence of copula as a functional category, as well as the role and degree of L1 influe...