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Topos Theory

Topos Theory Quiz

15 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

What is a topos?

  1. A category with a natural numbers object
  2. A category with a power object
  3. A category with a subobject classifier
  4. All of the above
Question 2 Multiple Choice (Single Answer)

What is the Yoneda embedding?

  1. A functor from a category to the category of presheaves on that category
  2. A functor from a category to the category of sheaves on that category
  3. A functor from a category to the category of sets
  4. A functor from a category to the category of groups
Question 3 Multiple Choice (Single Answer)

What is the Giraud-Lawvere theorem?

  1. A theorem that states that every topos is equivalent to a category of sheaves on a space
  2. A theorem that states that every topos is equivalent to a category of presheaves on a space
  3. A theorem that states that every topos is equivalent to a category of sets
  4. A theorem that states that every topos is equivalent to a category of groups
Question 4 Multiple Choice (Single Answer)

What is a Grothendieck topos?

  1. A topos that is equivalent to the category of sheaves on a scheme
  2. A topos that is equivalent to the category of sheaves on a manifold
  3. A topos that is equivalent to the category of sheaves on a topological space
  4. A topos that is equivalent to the category of sheaves on a set
Question 5 Multiple Choice (Single Answer)

What is an elementary topos?

  1. A topos that is generated by a set of generators and relations
  2. A topos that is generated by a set of generators and equational axioms
  3. A topos that is generated by a set of generators and universal Horn sentences
  4. A topos that is generated by a set of generators and existential sentences
Question 6 Multiple Choice (Single Answer)

What is the internal logic of a topos?

  1. The first-order logic of the topos
  2. The second-order logic of the topos
  3. The infinitary logic of the topos
  4. The intuitionistic logic of the topos
Question 7 Multiple Choice (Single Answer)

What is the topos of sets?

  1. The category of sets
  2. The category of presheaves on the category of sets
  3. The category of sheaves on the category of sets
  4. The category of Grothendieck toposes
Question 8 Multiple Choice (Single Answer)

What is the topos of sheaves on a space?

  1. The category of sheaves on the space
  2. The category of presheaves on the space
  3. The category of Grothendieck toposes
  4. The category of sets
Question 9 Multiple Choice (Single Answer)

What is the topos of presheaves on a space?

  1. The category of presheaves on the space
  2. The category of sheaves on the space
  3. The category of Grothendieck toposes
  4. The category of sets
Question 10 Multiple Choice (Single Answer)

What is the topos of Grothendieck toposes?

  1. The category of Grothendieck toposes
  2. The category of sheaves on the category of Grothendieck toposes
  3. The category of presheaves on the category of Grothendieck toposes
  4. The category of sets
Question 11 Multiple Choice (Single Answer)

What is the topos of elementary toposes?

  1. The category of elementary toposes
  2. The category of sheaves on the category of elementary toposes
  3. The category of presheaves on the category of elementary toposes
  4. The category of sets
Question 12 Multiple Choice (Single Answer)

What is the topos of internal sets in a topos?

  1. The category of internal sets in the topos
  2. The category of sheaves on the category of internal sets in the topos
  3. The category of presheaves on the category of internal sets in the topos
  4. The category of sets
Question 13 Multiple Choice (Single Answer)

What is the topos of internal sheaves in a topos?

  1. The category of internal sheaves in the topos
  2. The category of sheaves on the category of internal sheaves in the topos
  3. The category of presheaves on the category of internal sheaves in the topos
  4. The category of sets
Question 14 Multiple Choice (Single Answer)

What is the topos of internal presheaves in a topos?

  1. The category of internal presheaves in the topos
  2. The category of sheaves on the category of internal presheaves in the topos
  3. The category of presheaves on the category of internal presheaves in the topos
  4. The category of sets
Question 15 Multiple Choice (Single Answer)

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

  1. The category of internal Grothendieck toposes in the topos
  2. The category of sheaves on the category of internal Grothendieck toposes in the topos
  3. The category of presheaves on the category of internal Grothendieck toposes in the topos
  4. The category of sets
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