nLab cocartesian monoidal category

Contents

Context

Monoidal categories

monoidal categories

With braiding

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 cocartesian monoidal category is a monoidal category (𝒞,0,)\big(\mathcal{C}, 0, \sqcup \big) whose monoidal product functor :𝒞×𝒞𝒞\sqcup \,\colon\, \mathcal{C} \times \mathcal{C} \to \mathcal{C} is given by the coproduct (and so whose tensor unit is an initial object00”).

This is the dual notion of that of a cartesian monoidal category.

Sometime we refer to a category as cocartesian monoidal just to indicate that it has all finite coproducts.

References

The terminology appears for instance in:

Last revised on February 22, 2024 at 08:23:51. See the history of this page for a list of all contributions to it.