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I seemed to remember that somewhere on the Lab we had spelled out the full argument that for an -topos presented by a model structure on simplicial sheaves, then the relative Postnikov tower of any morphism is presented by applying objectwise the relative Postnikov tower of maps of simplicial sets (as e.g. in Goerss-Jardine VI. def. 2.9). But now I can’t find it.
I feel I can add something to this discussion for Postnikov towers as induced by chains of factorization systems. Hope to find the time during the holidays.
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