Background
Basic concepts
equivalences in/of $(\infty,1)$-categories
Universal constructions
Local presentation
Theorems
Extra stuff, structure, properties
Models
With braiding
With duals for objects
category with duals (list of them)
dualizable object (what they have)
ribbon category, a.k.a. tortile category
With duals for morphisms
monoidal dagger-category?
With traces
Closed structure
Special sorts of products
Semisimplicity
Morphisms
Internal monoids
Examples
Theorems
In higher category theory
A cocartesian monoidal (∞,1)-category is a symmetric monoidal (∞,1)-category whose tensor product is given by the categorical coproduct. This is dual to the notion of cartesian monoidal (∞,1)-category.
(…)
(…)
If $C$ is an (infinity,1)-category admitting finite coproducts, then the cocartesian symmetric monoidal structure on $C$ is equivalent to the symmetric monoidal structure obtained as the opposite of the cartesian monoidal structure on the opposite (infinity,1)-category $C^{op}$.
If $C$ is an (infinity,1)-category with finite coproducts, then the cocartesian model structure on $C$ is universal among symmetric monoidal (infinity,1)-categories $D$ for which there exists a functor $C \to CAlg(D)$, to the symmetric monoidal (infinity,1)-category of commutative algebra objects in $D$.
See (Lurie, Theorme 2.4.3.18).
Section 2.4 of
Created on March 6, 2015 at 18:05:52. See the history of this page for a list of all contributions to it.