Premium
Uncountable Orthogonality is a Closure Property
Author(s) -
Hébert M.,
Rosický J.
Publication year - 2001
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609301008451
Subject(s) - uncountable set , mathematics , orthogonality , closure (psychology) , property (philosophy) , statement (logic) , surprise , pure mathematics , calculus (dental) , geometry , epistemology , countable set , social psychology , medicine , philosophy , economics , market economy , psychology , dentistry
It is shown that, for λ > ω, λ‐orthogonality classes in locally λ‐presentable categories coincide with full subcategories that are closed under limits and under λ‐directed colimits. This comes as a surprise, since the statement is known to be false for λ = ω. 2000 Mathematics Subject Classification 18C35, 03G30, 18A40, 03C99.