# nLab absorption category

Contents

### Context

#### Algebra

higher algebra

universal algebra

category theory

categorification

# Contents

## Idea

The concept of an absorption category should be the oidification of an absorption monoid.

## Definition

An absorption category or annihilation category $C$ is a category where for every two objects $a, b \in Ob(C)$ there is a morphism $0_{a\to b}: a \to b$, such that for any objects $a, b, c, d \in Ob(C)$, for any morphism $f:b \to c$, $f \circ 0_{a\to b} = 0_{a\to c}$, and for any morphism $g:d \to a$, $0_{a\to b} \circ g = 0_{d\to b}$.

Such a structure is the same thing as a category enriched in the category of pointed sets, taking the monoidal product to be the smash product.

## Examples

Last revised on June 18, 2021 at 18:33:33. See the history of this page for a list of all contributions to it.