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

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

out of the coproduct, induced from the commuting diagram

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

Revised on January 11, 2014 22:18:12 by Andrej Bauer? (193.77.148.136)