An Essential Local Geometric Morphism which is not Locally Connected though its Inverse Image Part defines an Exponential Ideal

TL;DR

This paper constructs an example of a local geometric morphism that is essential but not locally connected, yet its inverse image part forms an exponential ideal, highlighting a nuanced distinction in topos theory.

Contribution

It introduces a specific example of an essential local geometric morphism lacking local connectedness, expanding understanding of morphism properties in topos theory.

Findings

The morphism is essential but not locally connected.

Its inverse image part forms an exponential ideal.

The example clarifies distinctions in morphism properties.

Abstract

We describe an essential local geometric morphism which is not locally connected, though its inverse image part defines an exponential ideal