{'fraction_non_alphanumeric': 0.011961722488038277, 'fraction_numerical': 0.0, 'mean_word_length': 4.586666666666667, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Aspects of slice stability in locale theory

Abstract. It is shown that a particular categorical axiomatisation of the category of locales is slice stable. This localic slice stability can be used to recover the fundamental theorem of topos theory. A categorical account of the ideal completion of a preorder is developed and is used to give a new proof of Joyal and Tierney's result on the slice stability of locales.