directed colimit
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2018 ◽  
Vol 16 (1) ◽  
pp. 669-687
Author(s):  
Xingliang Liang ◽  
Roghaieh Khosravi

AbstractLet S be a pomonoid. In this paper, we introduce some new types of epimorphisms with certain purity conditions, and obtain equivalent descriptions of various flatness properties of S-posets, such as strong flatness, Conditions (E), (E′), (P), (Pw), (WP), (WP)w, (PWP) and (PWP)w. Thereby, we present other equivalent conditions in the Stenström-Govorov-Lazard theorem for S-posets. Furthermore, we prove that these new epimorphisms are closed under directed colimits. Meantime, this implies that by a new approach we can show that most of flatness properties of S-posets can be transferred to their directed colimit. Finally, we prove that every class of S-posets having a flatness property is closed under directed colimits.


Author(s):  
R. PARÉ ◽  
J. ROSICKÝ

AbstractWe show that any directed colimit of accessible categories and accessible full embeddings is accessible and, assuming the existence of arbitrarily large strongly compact cardinals, any directed colimit of accessible categories and accessible embeddings is accessible.


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