Dugger : universal homotopy theories

Henosophia TOPOSOPHIA μαθεσις uni√ersalis τοποσοφια MATHESIS οντοποσοφια ενοσοφια Philosophie, théorie des catégories et théorie homotopique des types


Papier cité dans ce lien :


En compagnie de cet autre article


Un lien est donné vers une autre page de mathoverflow :


où l’on trouve ces précisions

« Model categories are 1-categorical presentations of (∞,1)-categories, which you can just think of as categories enriched in topological spaces, such as the category of spaces itself. (Actually, there are conditions on (∞,1)-categories that come from model categories–most importantly they must have all homotopy limits and colimits«

Deux autres papiers sont cités :



« In this paper, Theorem 2.5.9, it is shown that every model category (not necessarily a combinatorial one) has all limits and colimits. However, it is not hard to find examples of model categories whose underlying ∞
-categories are neither presentable nor co-presentable. For instance, Isaksen’s strict model structure on pro-simplicial sets. It is shown in the paper mentioned above that the underlying ∞

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