mono confusion

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when toggle format	what		by	license	comment
Dec 1, 2017 at 10:43	vote	accept	მამუკა ჯიბლაძე
Dec 1, 2017 at 9:37	history	edited	Yonatan Harpaz	CC BY-SA 3.0	added 148 characters in body
Dec 1, 2017 at 9:02	comment	added	Yonatan Harpaz		For the construction of truncated model structures in categories of simplicial presheaves see Biedermann, On the homotopy theory of $n$-types. You can also look in the section on truncation in Rezk's toposes and homotopy toposes. The truncated model structure is obtained as a left Bousfield localization, so it's always related to the original one by a Quillen adjunction. As for cotruncation, cotruncated objects in $\infty$-topoi are very rare (in spaces it's only the empty set), but they do appear in other cases. For example, in rings the (-1)-cotruncated objects are the solid rings.
Dec 1, 2017 at 5:20	comment	added	მამუკა ჯიბლაძე		I like this very much, thanks! Can you provide any references? Do you know if this is functorial, providing an adjunction(reflection?)? Is there, driving analogy with skeleta and coskeleta of simplicial sets, also a co-truncation, giving another adjoint? Are there also (co)truncations at other levels?
Nov 30, 2017 at 21:46	history	answered	Yonatan Harpaz	CC BY-SA 3.0