Approximate injectivity

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F18%3A00101081" target="_blank" >RIV/00216224:14310/18:00101081 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s10485-017-9510-2" target="_blank" >http://dx.doi.org/10.1007/s10485-017-9510-2</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10485-017-9510-2" target="_blank" >10.1007/s10485-017-9510-2</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Approximate injectivity

Popis výsledku v původním jazyce

In a locally $lambda$-presentable category, with $lambda$ a regular cardinal, classes of objects that are injective with respect to a family of morphisms whose domains and codomains are $lambda$-presentable, are known to be characterized by their closure under products, $lambda$-directed colimits and $lambda$-pure subobjects. Replacing the strict commutativity of diagrams by ``commutativity up to $eps$", this paper provides an ``approximate version" of this characterization for categories enriched over metric spaces. It entails a detailed discussion of the needed $eps$-generalizations of the notion of $lambda$-purity. The categorical theory is being applied to the locally $aleph_1$-presentable category of Banach spaces and their linear operators of norm at most 1, culminating in a largely categorical proof for the existence of the so-called Gurarii Banach space.

Název v anglickém jazyce

Approximate injectivity

Popis výsledku anglicky

In a locally $lambda$-presentable category, with $lambda$ a regular cardinal, classes of objects that are injective with respect to a family of morphisms whose domains and codomains are $lambda$-presentable, are known to be characterized by their closure under products, $lambda$-directed colimits and $lambda$-pure subobjects. Replacing the strict commutativity of diagrams by ``commutativity up to $eps$", this paper provides an ``approximate version" of this characterization for categories enriched over metric spaces. It entails a detailed discussion of the needed $eps$-generalizations of the notion of $lambda$-purity. The categorical theory is being applied to the locally $aleph_1$-presentable category of Banach spaces and their linear operators of norm at most 1, culminating in a largely categorical proof for the existence of the so-called Gurarii Banach space.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GBP201%2F12%2FG028" target="_blank" >GBP201/12/G028: Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku</a><br>

Návaznosti

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

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

Applied Categorical Structures

ISSN

0927-2852

e-ISSN

—

Svazek periodika

26

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

18

Strana od-do

699-716

Kód UT WoS článku

000437673800006

EID výsledku v databázi Scopus

2-s2.0-85038356732