nLab multirepresentable functor

Contents

Contents

Definition

A functor F:CSetF : 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.

References

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)

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