# nLab cartesian monoidal (infinity,1)-category

### Context

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

(∞,1)-category theory

## Models

#### Monoidal categories

monoidal categories

# 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.

(…)

(…)

## 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.

Section 2.4 of