Approximate injectivity and smallness in metric-enriched categories

Kód výsledku v IS VaVaI

RIV/00216224:14310/22:00119372 - isvavai.cz

Nalezeny alternativní kódy

RIV/68407700:21230/22:00360032

Výsledek na webu

https://www.sciencedirect.com/science/article/pii/S0022404921003157?via%3Dihub

DOI - Digital Object Identifier

10.1016/j.jpaa.2021.106974

Jazyk výsledku

angličtina

Název v původním jazyce

Approximate injectivity and smallness in metric-enriched categories

Popis výsledku v původním jazyce

Properties of categories enriched over the category of metric spaces are investigated and applied to a study of well-known constructions of metric and Banach spaces. We prove e.g. that weighted limits and colimits exist in a metric-enriched category iff ordinary limits and colimits exist and ε-(co)equalizers are given by ε-(co)isometries for all ε. An object is called approximately injective w.r.t. a morphism h : A -> A' iff morphisms from A into it are arbitrarily close to those morphisms that factorize through h. We investigate classes of objects specified by their approximate injectivity w.r.t. given morphisms. They are called approximate-injectivity classes. And we also study, conversely, classes of morphisms specified by the property that certain objects are approximately injective w.r.t. them. For every class of morphisms satisfying a mild smallness condition we prove that the corresponding approximate-injectivity class is weakly reflective, and we study the properties of the reflection morphisms. As an application we present a new categorical proof of the essential uniqueness of the Gurarii space.

Název v anglickém jazyce

Approximate injectivity and smallness in metric-enriched categories

Popis výsledku anglicky

Properties of categories enriched over the category of metric spaces are investigated and applied to a study of well-known constructions of metric and Banach spaces. We prove e.g. that weighted limits and colimits exist in a metric-enriched category iff ordinary limits and colimits exist and ε-(co)equalizers are given by ε-(co)isometries for all ε. An object is called approximately injective w.r.t. a morphism h : A -> A' iff morphisms from A into it are arbitrarily close to those morphisms that factorize through h. We investigate classes of objects specified by their approximate injectivity w.r.t. given morphisms. They are called approximate-injectivity classes. And we also study, conversely, classes of morphisms specified by the property that certain objects are approximately injective w.r.t. them. For every class of morphisms satisfying a mild smallness condition we prove that the corresponding approximate-injectivity class is weakly reflective, and we study the properties of the reflection morphisms. As an application we present a new categorical proof of the essential uniqueness of the Gurarii space.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

GA19-00902S: Injektivita a monády v algebře a topologii

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Pure and Applied Algebra

ISSN

0022-4049

e-ISSN

—

Svazek periodika

226

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

30

Strana od-do

106974

Kód UT WoS článku

000744249900002

EID výsledku v databázi Scopus

2-s2.0-85119609485