category theory

# Contents

## Definition

Let $\otimes : \mathcal{E}_1 \times \mathcal{E}_2 \to \mathcal{E}_3$ be a functor (e.g. a tensor product, tensoring). Let $\mathcal{E}_3$ have pushouts.

###### Definition

For $f : A \to B$ in $\mathcal{E}_1$ and $g : X \to Y$ in $\mathcal{E}_2$, the pushout product morphism is the morphism

$A \otimes Y \coprod_{A \otimes X} B \otimes X \to B \otimes Y$

out of the coproduct, induced from the commuting diagram

$\array{ A \otimes X &\to& B \otimes X \\ \downarrow && \downarrow \\ A \otimes Y &\to& B \otimes Y } \,.$

Revised on March 14, 2014 05:19:43 by Anonymous Coward (137.73.14.7)