### Abstract

The usual statements of the classical adjoint-functor theorems contain the hypothesis that the codomain category should admit arbitrary intersections of families of monomorphisms with a common codomain. The aim of this article is to formulate an adjoint-functor theorem which refers, in a similar manner, to arbitrary internal intersections of “families of monomorphisms” in the case where the categories under consideration are suitably defined relative to a fixed elementary base topos (in the usual sense of Lawvere and Tierney).

Original language | English |
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Pages (from-to) | 381-394 |

Number of pages | 14 |

Journal | Bulletin of the Australian Mathematical Society |

Volume | 15 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1976 |

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## Cite this

Day, B. J. (1976). An adjoint-functor theorem over topoi.

*Bulletin of the Australian Mathematical Society*,*15*(3), 381-394. https://doi.org/10.1017/S0004972700022814