Publication details

Internal sizes in mu-abstract elementary classes

Investor logo

LIEBERMAN Michael ROSICKÝ Jiří VASEY Sébastien Bernard

Year of publication 2019
Type Article in Periodical
Magazine / Source Journal of Pure and Applied Algebra
MU Faculty or unit

Faculty of Science

Keywords accessible category; internal size; abstract ekementary class
Description 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.
Related projects:

You are running an old browser version. We recommend updating your browser to its latest version.

More info