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This is a mostly question for Zoran in particular as he is nearest to the Shape considerations where it occurs. Goerss and Jardine discuss towers of simplicial sets and a model category structure on them, but their morphisms are not those of the structure needed for pro-categories (i.e. as per Grossman’s paper and more recently Isaksen’s model structure on Pro-sSet.) If we are to discuss those latter ones somewhere, (and it would seem natural to do so) then there needs to be some convention on which is which! Any ideas? At present in the Lab, towers refer only to the functor category à là Goerss-Jardine.
Yep. The sneaky Grossman structure is obtained from the one use by Goerss and Jardine by localising with respect to the natural maps from a space to its Postnikov tower (more or less).
I see the question only now. Will try to think later, I have no immediate comments. Interesting gadget.
I have added to tower a section The pro-category of towers. So far it contains just the definition, the statement that all pro-morphisms of towers are represented by towers of morphisms (proof?) and the statement that finite limits and colimits are represented by degreewise such under this presentation.
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