Return to Question

Bounded geometric morphisms serve as a generalization of Grothendieck topoi; $T$ being a Grothendieck topos iff global section $T \rightarrow Set$ is bounded. I managed to only track this down to the Johnstone's, 1977 Topos theory, where it is defined, but the terminology "bound"/"bounded" isn't motivated. The definition of Bounded geometric morphism 4.43, is attributed to "W. Mitchell", but none of the 3 references by Mitchell (William Mitchell, the only Mitchell in the bibliography as a sole author) in the bibliography seem to use the terms "bound"/"bounded" or discuss a similar definition on a skim.

This results in 2 questions: What's the motivation for calling these geometric morphisms bounded, calling part of the definition a "bound"? What's the original text defining and hopefully motivating the terminology "bounded"?

The 3 references by William Mitchell being:

1. "Categories of Boolean Topoi"
2. "On topoi as closed categories"
3. "Boolean topoi and the theory of sets"

Bounded geometric morphisms serve as a generalization of Grothendieck topoi; $T$ being a Grothendieck topos iff global section $T \rightarrow Set$ is bounded. I managed to only track this down to the Johnstone's, 1977 Topos theory, where it is defined, but the terminology "bound"/"bounded" isn't motivated. The definition of Bounded geometric morphism 4.43, is attributed to "W. Mitchell", but none of the 3 references by Mitchell (William Mitchell, the only Mitchell in the bibliography as a sole author) in the bibliography seem to use the terms "bound"/"bounded" or discuss a similar definition on a skim.

This results in 3 questions:

1. What's the motivation for calling these geometric morphisms bounded, calling part of the definition a "bound"?
2. What's the original text defining and hopefully motivating the terminology "bounded"?
3. Is there a precise connection with order theoretical bounded?

The 3 references by William Mitchell being:

1. "Categories of Boolean Topoi"
2. "On topoi as closed categories"
3. "Boolean topoi and the theory of sets"

Bounded geometric morphisms serve as a generalization of Grothendieck topoi; $T$ being a Grothendieck topos iff global section $T \rightarrow Set$ is bounded. I managed to only track this down to the Johnstone's, 1977 Topos theory, where it is defined, but the terminology "bound"/"bounded" isn't motivated. The definition of Bounded geometric morphism 4.43, is attributed to "W. Mitchell", but none of the 3 references by Mitchell (William Mitchell, the only Mitchell in the bibliography as a sole author) in the bibliography seem to use the terms "bound"/"bounded" or discuss a similar definition on a skim.

This results in 2 questions: What's the motivation for calling these geometric morphisms bounded, calling part of the definition a "bound"? what's the original text defining and hopefully motivating the terminology "bounded"?

The 3 references by William Mitchell being:

1. "Categories of Boolean Topoi"
2. "On topoi as closed categories"
3. "Boolean topoi and the theory of sets"

Bounded geometric morphisms serve as a generalization of Grothendieck topoi; $T$ being a Grothendieck topos iff global section $T \rightarrow Set$ is bounded. I managed to only track this down to the Johnstone's, 1977 Topos theory, where it is defined, but the terminology "bound"/"bounded" isn't motivated. The definition of Bounded geometric morphism 4.43, is attributed to "W. Mitchell", but none of the 3 references by Mitchell (William Mitchell, the only Mitchell in the bibliography as a sole author) in the bibliography seem to use the terms "bound"/"bounded" or discuss a similar definition on a skim.

This results in 2 questions: What's the motivation for calling these geometric morphisms bounded, calling part of the definition a "bound"? What's the original text defining and hopefully motivating the terminology "bounded"?

The 3 references by William Mitchell being:

1. "Categories of Boolean Topoi"
2. "On topoi as closed categories"
3. "Boolean topoi and the theory of sets"

Bounded geometric morphisms serve as a generalization of Grothendieck topoi; $T$ being a Grothendieck topos iff global section $T \rightarrow Set$ is bounded. I managed to only track this down to the Johnstone's, 1977 Topos theory, where it is defined, but the terminology "bound"/"bounded" isn't motivated. The definition of Bounded geometric morphism 4.43, is attributed to "W. Mitchell", but none of the 3 references by Mitchell (William Mitchell, the only Mitchell in the bibliography as a sole author) in the bibliography seem to use the terms "bound"/"bounded".

This results in 2 questions: What's the motivation for calling these geometric morphisms bounded, calling part of the definition a "bound"? what's the original text defining and hopefully motivating the terminology "bounded"?

The 3 references by William Mitchell being:

1. "Categories of Boolean Topoi"
2. "On topoi as closed categories"
3. "Boolean topoi and the theory of sets"

Bounded geometric morphisms serve as a generalization of Grothendieck topoi; $T$ being a Grothendieck topos iff global section $T \rightarrow Set$ is bounded. I managed to only track this down to the Johnstone's, 1977 Topos theory, where it is defined, but the terminology "bound"/"bounded" isn't motivated. The definition of Bounded geometric morphism 4.43, is attributed to "W. Mitchell", but none of the 3 references by Mitchell (William Mitchell, the only Mitchell in the bibliography as a sole author) in the bibliography seem to use the terms "bound"/"bounded" or discuss a similar definition on a skim.

This results in 2 questions: What's the motivation for calling these geometric morphisms bounded, calling part of the definition a "bound"? what's the original text defining and hopefully motivating the terminology "bounded"?

The 3 references by William Mitchell being:

1. "Categories of Boolean Topoi"
2. "On topoi as closed categories"
3. "Boolean topoi and the theory of sets"