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@article{1527257,
author = {Lieberman, Michael and Rosický, Jiří and Vasey, Sébastien Bernard},
article_location = {AMSTERDAM},
article_number = {10},
doi = {http://dx.doi.org/10.1016/j.jpaa.2019.02.004},
keywords = {accessible category; internal size; abstract ekementary class},
language = {eng},
issn = {0022-4049},
journal = {Journal of Pure and Applied Algebra},
title = {Internal sizes in mu-abstract elementary classes},
url = {http://people.math.harvard.edu/~sebv/papers/lrv-sizes/lrv-sizes_v4.pdf},
volume = {223},
year = {2019}
}
TY - JOUR
ID - 1527257
AU - Lieberman, Michael - Rosický, Jiří - Vasey, Sébastien Bernard
PY - 2019
TI - Internal sizes in mu-abstract elementary classes
JF - Journal of Pure and Applied Algebra
VL - 223
IS - 10
SP - 4560-4582
EP - 4560-4582
PB - ELSEVIER
SN - 00224049
KW - accessible category
KW - internal size
KW - abstract ekementary class
UR - http://people.math.harvard.edu/~sebv/papers/lrv-sizes/lrv-sizes_v4.pdf
L2 - http://people.math.harvard.edu/~sebv/papers/lrv-sizes/lrv-sizes_v4.pdf
N2 - Working in the context of $\mu$-abstract elementary classes or, equivalently, accessible categories with all morphisms monomorphisms, we examine the two natural notions of size that occur, namely cardinality of underlying sets and internal size. The latter, purely category-theoretic, notion generalizes e.g. density character in complete metric spaces and cardinality of orthogonal bases in Hilbert spaces. We consider the relationship between these notions under mild set-theoretic hypotheses, including weakenings of the singular cardinal hypothesis.
ER -
LIEBERMAN, Michael, Jiří ROSICKÝ a Sébastien Bernard VASEY. Internal sizes in mu-abstract elementary classes. \textit{Journal of Pure and Applied Algebra}. AMSTERDAM: ELSEVIER, 2019, roč.~223, č.~10, s.~4560-4582. ISSN~0022-4049. Dostupné z: https://dx.doi.org/10.1016/j.jpaa.2019.02.004.
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