Density in categorical topology via quantaloid-enriched categories
نویسندگان
چکیده
منابع مشابه
Categorical structures enriched in a quantaloid: projective cocomplete categories
We study the different guises of the projective objects in Cocont(Q): they are the “completely distributive” cocomplete Q-categories (the left adjoint to the Yoneda embedding admits a further left adjoint); equivalently, they are the “totally continuous” cocomplete Q-categories (every object is the supremum of the presheaf of objects “totally below” it); and also are they the Q-categories of re...
متن کاملCategorical Structures Enriched in a Quantaloid: Categories, Distributors and Functors
We thoroughly treat several familiar and less familiar definitions and results concerning categories, functors and distributors enriched in a base quantaloidQ. In analogy with V-category theory we discuss such things as adjoint functors, (pointwise) left Kan extensions, weighted (co)limits, presheaves and free (co)completion, Cauchy completion and Morita equivalence. With an appendix on the uni...
متن کاملCategorical Structures Enriched in a Quantaloid: Tensored and Cotensored Categories
A quantaloid is a sup-lattice-enriched category; our subject is that of categories, functors and distributors enriched in a base quantaloid Q. We show how cocomplete Q-categories are precisely those which are tensored and conically cocomplete, or alternatively, those which are tensored, cotensored and ‘order-cocomplete’. In fact, tensors and cotensors in a Q-category determine, and are determin...
متن کاملAn introduction to quantaloid-enriched categories
This survey paper, specifically targeted at a readership of fuzzy logicians and fuzzy set theorists, aims to provide a gentle introduction to the basic notions of quantaloidenriched category theory. We discuss at length the definitions of quantaloid, quantaloidenriched category, distributor and functor, always giving several examples that – hopefully – appeal to the intended readership. To indi...
متن کاملExponentiable Functors Between Quantaloid-Enriched Categories
Exponentiable functors between quantaloid-enriched categories are characterized in elementary terms. The proof goes as follows: the elementary conditions on a given functor translate into existence statements for certain adjoints that obey some lax commutativity; this, in turn, is precisely what is needed to prove the existence of partial products with that functor; so that the functor’s expone...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2020
ISSN: 0166-8641
DOI: 10.1016/j.topol.2020.107524