equivalences in/of $(\infty,1)$-categories
Work on $\infty$-category and $(\infty,1)$-category theory often uses the implicit $\infty$-category theory convention, leaving out the “$\infty$” or “$(\infty,1)$” symbol in notation and terminology.
In this convention
category means (∞,1)-category, and so $Cat$ means (∞,1)Cat
topos means (∞,1)-topos, and so $Topos$ means (∞,1)Topos
groupoid means ∞-groupoid, and so $Gpd$ means ?Gpd?
$n$-category means (∞,n)-category
functor means (∞,1)-functor or (∞,n)-functor for some $n \in \mathbb{N}$, depending on the codomain;
presheaf means (∞,1)-presheaf,
sheaf means (∞,1)-sheaf , a.k.a. ∞-stack
limit means (∞,1)-limit
algebraic theory means (∞,1)-algebraic theory
algebra over an algebraic theory means ∞-algebra over an (∞,1)-algebraic theory .
Etc.
This convention is used for example by Jacob Lurie and often on nLab entries that discuss higher category theory.
(Note that this convention never applies to the names of pages in the Lab; see Naming conventions. That also means that when writing pages using this convention, one must be sure to use the appropriate “pipelinks,” such as <a class='existingWikiWord' href='/nlab/show/%28infinity%2C1%29-topos'>topos</a>
.)
Last revised on March 2, 2018 at 15:55:19. See the history of this page for a list of all contributions to it.