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Category Theory Foundations

Quiz covering fundamental and advanced concepts in category theory including categories, functors, natural transformations, and key theorems.

13 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

What is a category?

  1. A collection of objects and arrows.
  2. A set of sets.
  3. A group of transformations.
  4. A topological space.
Question 2 Multiple Choice (Single Answer)

What is a functor?

  1. A function between categories.
  2. A transformation between functors.
  3. A natural transformation between functors.
  4. A category of functors.
Question 3 Multiple Choice (Single Answer)

What is a natural transformation?

  1. A transformation between functors.
  2. A function between categories.
  3. A category of functors.
  4. A set of natural numbers.
Question 4 Multiple Choice (Single Answer)

What is an adjoint functor?

  1. A functor that has a right adjoint.
  2. A functor that has a left adjoint.
  3. A functor that has both a left and right adjoint.
  4. A functor that has no adjoints.
Question 5 Multiple Choice (Single Answer)

What is a monoidal category?

  1. A category with a tensor product.
  2. A category with a unit object.
  3. A category with a zero object.
  4. A category with a product and a coproduct.
Question 6 Multiple Choice (Single Answer)

What is a closed category?

  1. A category with a tensor product and an internal hom functor.
  2. A category with a unit object and a zero object.
  3. A category with a product and a coproduct.
  4. A category with a power object.
Question 7 Multiple Choice (Single Answer)

What is a topos?

  1. A category that is locally cartesian closed.
  2. A category that is cartesian closed.
  3. A category that is monoidal closed.
  4. A category that is symmetric monoidal closed.
Question 8 Multiple Choice (Single Answer)

What is the Yoneda lemma?

  1. A result that relates functors to natural transformations.
  2. A result that relates categories to sets.
  3. A result that relates functors to categories.
  4. A result that relates natural transformations to categories.
Question 9 Multiple Choice (Single Answer)

What is the coherence theorem?

  1. A result that shows that the category of categories is cartesian closed.
  2. A result that shows that the category of categories is monoidal closed.
  3. A result that shows that the category of categories is symmetric monoidal closed.
  4. A result that shows that the category of categories is locally cartesian closed.
Question 10 Multiple Choice (Single Answer)

What is the Giraud-Weibel theorem?

  1. A result that shows that every topos is equivalent to a category of sheaves.
  2. A result that shows that every category of sheaves is equivalent to a topos.
  3. A result that shows that every topos is equivalent to a category of presheaves.
  4. A result that shows that every category of presheaves is equivalent to a topos.
Question 11 Multiple Choice (Single Answer)

What is the Stone duality theorem?

  1. A result that relates Boolean algebras to topological spaces.
  2. A result that relates Boolean algebras to sets.
  3. A result that relates Boolean algebras to categories.
  4. A result that relates Boolean algebras to natural transformations.
Question 12 Multiple Choice (Single Answer)

What is the Mac Lane coherence theorem?

  1. A result that shows that the category of categories is symmetric monoidal closed.
  2. A result that shows that the category of categories is cartesian closed.
  3. A result that shows that the category of categories is monoidal closed.
  4. A result that shows that the category of categories is locally cartesian closed.
Question 13 Multiple Choice (Single Answer)

What is the Kan extension?

  1. A functor that extends a functor from a small category to a larger category.
  2. A functor that extends a functor from a large category to a smaller category.
  3. A functor that extends a functor from a category to a set.
  4. A functor that extends a functor from a set to a category.
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