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 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. See also at (infinity,n)-category of correspondences the section Via coalgebras.
Section 2.4 of
Last revised on March 2, 2017 at 11:02:01. See the history of this page for a list of all contributions to it.