Background
Basic concepts
equivalences in/of -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 cartesian monoidal (∞,1)-category is a symmetric monoidal (∞,1)-category whose tensor product is given by the categorical product. This is dual to the notion of cocartesian monoidal (∞,1)-category.
In the special case that the underlying (∞,1)-category is equivalent to just a 1-category, then this is equivalently a cartesian monoidal category.
(…)
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Every object in a Cartesian monoidal -category is canonically a comonoid object via the diagonal map (just as in the 1-categorical case here).
See also at (infinity,n)-category of correspondences the section Via coalgebras.
Section 2.4 of
Last revised on August 25, 2023 at 16:04:58. See the history of this page for a list of all contributions to it.