category theory

# Contents

## Definition

Let $\otimes :{ℰ}_{1}×{ℰ}_{2}\to {ℰ}_{3}$ be a functor (e.g. a tensor product, tensoring). Let ${ℰ}_{3}$ have pushouts.

###### Definition

For $f:A\to B$ in ${ℰ}_{1}$ and $g:X\to Y$ in ${ℰ}_{2}$, the pushout product morphism is the morphism

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

out of the coproduct, induced from the commuting diagram

$\begin{array}{ccc}A\otimes X& \to & B\otimes X\\ ↓& & ↓\\ B\otimes X& \to & B\otimes Y\end{array}\phantom{\rule{thinmathspace}{0ex}}.$\array{ A \otimes X &\to& B \otimes X \\ \downarrow && \downarrow \\ B \otimes X &\to& B \otimes Y } \,.

Created on March 23, 2012 08:14:45 by Urs Schreiber (82.172.178.200)