Topos Theory Online Test

0

Topos Theory

Description: Topos Theory Quiz
Number of Questions: 15
Created by: Aliensbrain Bot
Tags: topos theory category theory algebraic geometry

What is a topos?

A category with a natural numbers object
A category with a power object
A category with a subobject classifier
All of the above

What is the Yoneda embedding?

A functor from a category to the category of presheaves on that category
A functor from a category to the category of sheaves on that category
A functor from a category to the category of sets
A functor from a category to the category of groups

What is the Giraud-Lawvere theorem?

A theorem that states that every topos is equivalent to a category of sheaves on a space
A theorem that states that every topos is equivalent to a category of presheaves on a space
A theorem that states that every topos is equivalent to a category of sets
A theorem that states that every topos is equivalent to a category of groups

What is a Grothendieck topos?

A topos that is equivalent to the category of sheaves on a scheme
A topos that is equivalent to the category of sheaves on a manifold
A topos that is equivalent to the category of sheaves on a topological space
A topos that is equivalent to the category of sheaves on a set

What is an elementary topos?

A topos that is generated by a set of generators and relations
A topos that is generated by a set of generators and equational axioms
A topos that is generated by a set of generators and universal Horn sentences
A topos that is generated by a set of generators and existential sentences

What is the internal logic of a topos?

The first-order logic of the topos
The second-order logic of the topos
The infinitary logic of the topos
The intuitionistic logic of the topos

What is the topos of sets?

The category of sets
The category of presheaves on the category of sets
The category of sheaves on the category of sets
The category of Grothendieck toposes

What is the topos of sheaves on a space?

The category of sheaves on the space
The category of presheaves on the space
The category of Grothendieck toposes
The category of sets

What is the topos of presheaves on a space?

The category of presheaves on the space
The category of sheaves on the space
The category of Grothendieck toposes
The category of sets

What is the topos of Grothendieck toposes?

The category of Grothendieck toposes
The category of sheaves on the category of Grothendieck toposes
The category of presheaves on the category of Grothendieck toposes
The category of sets

What is the topos of elementary toposes?

The category of elementary toposes
The category of sheaves on the category of elementary toposes
The category of presheaves on the category of elementary toposes
The category of sets

What is the topos of internal sets in a topos?

The category of internal sets in the topos
The category of sheaves on the category of internal sets in the topos
The category of presheaves on the category of internal sets in the topos
The category of sets

What is the topos of internal sheaves in a topos?

The category of internal sheaves in the topos
The category of sheaves on the category of internal sheaves in the topos
The category of presheaves on the category of internal sheaves in the topos
The category of sets

What is the topos of internal presheaves in a topos?

The category of internal presheaves in the topos
The category of sheaves on the category of internal presheaves in the topos
The category of presheaves on the category of internal presheaves in the topos
The category of sets

What is the topos of internal Grothendieck toposes in a topos?

The category of internal Grothendieck toposes in the topos
The category of sheaves on the category of internal Grothendieck toposes in the topos
The category of presheaves on the category of internal Grothendieck toposes in the topos
The category of sets

- Hide questions