Background
Basic concepts
equivalences in/of -categories
Universal constructions
Local presentation
Theorems
Extra stuff, structure, properties
Models
category with duals (list of them)
dualizable object (what they have)
ribbon category, a.k.a. tortile category
monoidal dagger-category?
A symmetric monoidal (∞,1)-category is closed if for each object the (∞,1)-functor
given by forming the tensor product with has a right adjoint (∞,1)-functor
(In cases where the monoidal structure is not assumed symmetric, the property of possessing a right adjoint to tensoring on the left (resp. right) is called left (resp. right) closed, while closed is used for the properties jointly (Def. Definition 4.1.1.15 of Higher Algebra).)
Every (∞,1)-topos with its structure of a cartesian monoidal (∞,1)-category is closed. See there for details.
The (∞,1)-category of (∞,1)-modules over an E-∞ ring is closed.
Last revised on May 26, 2022 at 18:07:59. See the history of this page for a list of all contributions to it.