nLab multirepresentable functor

Definition

A functor $F : C \to Set$ is multirepresentable if it is a coproduct of representable functors.

Properties

A functor is multirepresentable if and only if each connected component of its category of elements has an initial object: this is Proposition 2.1.2 of Diers 1977.

Related pages

• representable functor

• multiadjoint

References

• Yves Diers, Catégories localisables, PhD thesis. Paris 6 et Centre universitaire de Valenciennes et du Hainaut Cambrésis (1977) [Categories localisables.pdf]

Multirepresentable presheaves are called familially representable in:

• Aurelio Carboni, Peter Johnstone, Connected limits, familial representability and Artin glueing , Mathematical Structures in Computer Science 5 (1995) pp.441-459. (pdf)