nLab
pushout-product

Contents

Definition

Let : 1× 2 3 \otimes : \mathcal{E}_1 \times \mathcal{E}_2 \to \mathcal{E}_3 be a functor (e.g. a tensor product, tensoring). Let 3\mathcal{E}_3 have pushouts.

Definition

For f:ABf : A \to B in 1\mathcal{E}_1 and g:XYg : X \to Y in 2\mathcal{E}_2, the pushout product morphism is the morphism

AY AXBXBY A \otimes Y \coprod_{A \otimes X} B \otimes X \to B \otimes Y

out of the coproduct, induced from the commuting diagram

AX BX AY BY. \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)