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Category Theory and Computer Science

This quiz covers the fundamental concepts and applications of Category Theory in Computer Science.

15 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

In Category Theory, what is a functor?

  1. A mapping between categories that preserves structure
  2. A function between sets that preserves order
  3. A relation between elements of a category
  4. A transformation between functors
Question 2 Multiple Choice (Single Answer)

What is the Yoneda Lemma in Category Theory?

  1. Every functor from a category to the category of sets is uniquely determined by its values on the objects of the category
  2. Every category is equivalent to a category of sets
  3. Every functor is an isomorphism
  4. Every category has a unique initial object
Question 3 Multiple Choice (Single Answer)

What is a monad in Category Theory?

  1. A functor from a category to itself that preserves composition
  2. A functor from a category to the category of sets that preserves structure
  3. A natural transformation between two functors
  4. A category with a unique initial and terminal object
Question 4 Multiple Choice (Single Answer)

What is the Curry-Howard correspondence in Category Theory?

  1. A relationship between types and propositions in logic
  2. A connection between categories and sets
  3. A duality between functors and natural transformations
  4. An equivalence between monads and algebraic structures
Question 5 Multiple Choice (Single Answer)

What is a category in Category Theory?

  1. A collection of objects and morphisms between them
  2. A set of elements and relations between them
  3. A function between two sets
  4. A transformation between two functors
Question 6 Multiple Choice (Single Answer)

What is a natural transformation in Category Theory?

  1. A morphism between two functors
  2. A function between two sets that preserves structure
  3. A relation between elements of a category
  4. A transformation between categories
Question 7 Multiple Choice (Single Answer)

What is an initial object in a category?

  1. An object with a unique morphism from every other object
  2. An object with a unique morphism to every other object
  3. An object with no incoming morphisms
  4. An object with no outgoing morphisms
Question 8 Multiple Choice (Single Answer)

What is a terminal object in a category?

  1. An object with a unique morphism from every other object
  2. An object with a unique morphism to every other object
  3. An object with no incoming morphisms
  4. An object with no outgoing morphisms
Question 9 Multiple Choice (Single Answer)

What is a product in a category?

  1. An object that represents the Cartesian product of two objects
  2. An object that represents the disjoint union of two objects
  3. An object that represents the intersection of two objects
  4. An object that represents the symmetric difference of two objects
Question 10 Multiple Choice (Single Answer)

What is a coproduct in a category?

  1. An object that represents the Cartesian product of two objects
  2. An object that represents the disjoint union of two objects
  3. An object that represents the intersection of two objects
  4. An object that represents the symmetric difference of two objects
Question 11 Multiple Choice (Single Answer)

What is an equalizer in a category?

  1. An object that represents the intersection of two morphisms
  2. An object that represents the union of two morphisms
  3. An object that represents the composition of two morphisms
  4. An object that represents the difference of two morphisms
Question 12 Multiple Choice (Single Answer)

What is a coequalizer in a category?

  1. An object that represents the intersection of two morphisms
  2. An object that represents the union of two morphisms
  3. An object that represents the composition of two morphisms
  4. An object that represents the difference of two morphisms
Question 13 Multiple Choice (Single Answer)

What is a limit in a category?

  1. An object that represents the intersection of a diagram of objects
  2. An object that represents the union of a diagram of objects
  3. An object that represents the composition of a diagram of objects
  4. An object that represents the difference of a diagram of objects
Question 14 Multiple Choice (Single Answer)

What is a colimit in a category?

  1. An object that represents the intersection of a diagram of objects
  2. An object that represents the union of a diagram of objects
  3. An object that represents the composition of a diagram of objects
  4. An object that represents the difference of a diagram of objects
Question 15 Multiple Choice (Single Answer)

What is an adjunction in Category Theory?

  1. A pair of functors between two categories that are related by natural isomorphisms
  2. A pair of functors between two categories that are related by natural transformations
  3. A pair of functors between two categories that are related by equivalences
  4. A pair of functors between two categories that are related by isomorphisms
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