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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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