Abstract: It is a commonplace of higher category theory that, while every weak 2-category is equivalent to a strict 2-category, not every weak 3-category is equivalent to a strict 3-category. Nevertheless, the coherence theorem of Gordon, Power, and Street states that every weak 3-category is equivalent to a Gray-category (that is, a category enriched over the category of 2-categories equipped with Gray's symmetric monoidal structure). However, there are certain fundamental obstructions to the development of a purely Gray-enriched model for three-dimensional category theory. These obstructions may be overcome by the introduction of a new base for enrichment with more satisfactory technical properties: the cartesian closed model category of algebraically cofibrant 2-categories, which is the subject of this talk.
In this talk, Alexander will construct the model category of algebraically cofibrant 2-categories and explore several of its excellent properties. In particular, he will prove that its full subcategory of fibrant-cofibrant objects is equivalent to the category of bicategories and normal pseudofunctors, and that it is cartesian closed as a model category.
In person attendance is available in HN 1.33 for up to 52 people.
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