nLab
cartesian monoidal (infinity,1)-category

Contents

Context

(,1)(\infty,1)-Category theory

Monoidal categories

monoidal categories

With symmetry

With duals for objects

With duals for morphisms

With traces

Closed structure

Special sorts of products

Semisimplicity

Morphisms

Internal monoids

Examples

Theorems

In higher category theory

Contents

Idea

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.

Definition

(…)

(Lurie, def. 2.4.0.1)

(…)

Properties

Coalgebra objects

Every object in a Cartesian monoidal \infty-category is canonically a comonoid object via the diagonal map. See also at (infinity,n)-category of correspondences the section Via coalgebras.

References

Section 2.4 of

Last revised on March 2, 2017 at 06:02:01. See the history of this page for a list of all contributions to it.