nLab Surj

Idea

$Surj$ (or $Set_{surj}$) is the wide subcategory of the topos Set with its morphisms restricted to epimorphisms (surjective functions).

$FinSurj$ (or $FinSet_{surj}$) is the full subcategory of $Surj$ spanned by the finite sets. It is the free symmetric monoidal category generated by a commutative semigroup.

Related concepts

• Inj, FinInj

References

• Cole Comfort, A diagrammatic approach to networks of spans and relations, PhD thesis, University of Oxford, 2023, web.