nLab 1-category



Category theory

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higher category theory

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1-categorical presentations



In the context of higher category theory one sometimes needs, for emphasis, to say 1-category for category.


Fix a meaning of \infty-category, however weak or strict you wish. Then a 11-category is an \infty-category such that every 2-morphism is an equivalence and all parallel pairs of j-morphisms are equivalent for j2j \geq 2. Thus, up to equivalence, there is no point in mentioning anything beyond 11-morphisms, except whether two given parallel 11-morphisms are equivalent.

If you rephrase equivalence of 11-morphisms as equality, which gives the same result up to equivalence, then all that is left in this definition is a category. Thus one may also say that a 11-category is simply a category.

The point of all this is simply to fill in the general concept of nn-category; nobody thinks of 11-categories as a concept in their own right except simply as categories.

The notions of 11-groupoid and 11-poset are defined on the same basis.

Last revised on March 6, 2023 at 05:06:08. See the history of this page for a list of all contributions to it.