When coproducts are biproducts
Richard Garner, Daniel Sch\"appi
TL;DR
This paper characterizes when right-closed monoidal categories with finite coproducts have finite biproducts, extending Houston's result to a broader class of categories by identifying duality conditions.
Contribution
It provides a precise criterion involving duals for the existence of biproducts in right-closed monoidal categories with finite coproducts.
Findings
Categories with duals for initial object and coproduct of units have biproducts
Generalizes Houston's result to a wider class of categories
Characterizes biproducts via duality conditions
Abstract
Among right-closed monoidal categories with finite coproducts, we characterise those with finite biproducts as being precisely those in which the initial object and the coproduct of the unit with itself admit right duals. This generalises Houston's result that any compact closed category with finite coproducts admits biproducts.
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