Topological categories, quantaloids and Isbell adjunctions
نویسندگان
چکیده
منابع مشابه
Topological categories, quantaloids and Isbell adjunctions
In fairly elementary terms this paper presents, and expands upon, a recent result by Garner by which the notion of topologicity of a concrete functor is subsumed under the concept of total cocompleteness of enriched category theory. Motivated by some key results of the 1970s, the paper develops all needed ingredients from the theory of quantaloids in order to place essential results of categori...
متن کاملCategories Enriched over a Quantaloid: Isbell Adjunctions and Kan Adjunctions
Each distributor between categories enriched over a small quantaloid Q gives rise to two adjunctions between the categories of contravariant and covariant presheaves, and hence to two monads. These two adjunctions are respectively generalizations of Isbell adjunctions and Kan extensions in category theory. It is proved that these two processes are functorial with infomorphisms playing as morphi...
متن کاملAdjunctions Between Categories of Domains
In this paper we show that there is no left adjoint to the inclusion functor from the full subcategory C 0 of Scott domains (i.e., consistently complete ! algebraic cpo's) to SFP, the category of SFP-objects and Scott-continuous maps. We also show there is no left adjoint to the inclusion functor from C 0 to any larger category of cpo's which contains a simple ve-element domain. As a corollary,...
متن کاملHomotopy Coherent Adjunctions of Quasi-categories
We show that an adjoint functor between quasi-categories may be extended to a simplicially enriched functor whose domain is an explicitly presented “homotopy coherent adjunction”. This enriched functor encapsulates both the coherent monad and the coherent comonad generated by the adjunction. Furthermore, because its domain is cofibrant, this data can be used to construct explicit quasi-categori...
متن کاملON ALGEBRAIC AND COALGEBRAIC CATEGORIES OF VARIETY-BASED TOPOLOGICAL SYSTEMS
Motivated by the recent study on categorical properties of latticevalued topology, the paper considers a generalization of the notion of topological system introduced by S. Vickers, providing an algebraic and a coalgebraic category of the new structures. As a result, the nature of the category TopSys of S. Vickers gets clari ed, and a metatheorem is stated, claiming that (latticevalu...
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: 2016
ISSN: 0166-8641
DOI: 10.1016/j.topol.2015.12.020