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@article{1424262,
author = {Rosický, Jiří and Tholen, Walter},
article_number = {4},
doi = {http://dx.doi.org/10.1007/s10485-017-9510-2},
keywords = {enriched category; locally presentable category; pure morphism; injective object; approximate injectivity class; Urysohn space; Gurarii space},
language = {eng},
issn = {0927-2852},
journal = {Applied Categorical Structures},
title = {Approximate injectivity},
url = {http://dx.doi.org/10.1007/s10485-017-9510-2},
volume = {26},
year = {2018}
}
TY - JOUR
ID - 1424262
AU - Rosický, Jiří - Tholen, Walter
PY - 2018
TI - Approximate injectivity
JF - Applied Categorical Structures
VL - 26
IS - 4
SP - 699-716
EP - 699-716
SN - 09272852
KW - enriched category
KW - locally presentable category
KW - pure morphism
KW - injective object
KW - approximate injectivity class
KW - Urysohn space
KW - Gurarii space
UR - http://dx.doi.org/10.1007/s10485-017-9510-2
N2 - 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.
ER -
ROSICKÝ, Jiří a Walter THOLEN. Approximate injectivity. \textit{Applied Categorical Structures}. 2018, roč.~26, č.~4, s.~699-716. ISSN~0927-2852. Dostupné z: https://dx.doi.org/10.1007/s10485-017-9510-2.
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