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Category Theory

Test your understanding of fundamental and intermediate category theory concepts including categories, morphisms, functors, monads, limits/colimits, and the Yoneda lemma.

14 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

What is the fundamental concept in category theory?

  1. Category
  2. Object
  3. Morphism
  4. Functor
Question 2 Multiple Choice (Single Answer)

In category theory, what is a morphism?

  1. A mapping between objects in a category
  2. A function between sets
  3. A relation between elements of a set
  4. A transformation between vector spaces
Question 3 Multiple Choice (Single Answer)

What is the identity morphism in a category?

  1. The morphism that maps each object to itself
  2. The morphism that maps each object to the zero object
  3. The morphism that maps each object to the terminal object
  4. The morphism that maps each object to its inverse
Question 4 Multiple Choice (Single Answer)

What is a functor in category theory?

  1. A mapping between categories
  2. A function between sets
  3. A relation between elements of a set
  4. A transformation between vector spaces
Question 5 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 morphisms to objects
  4. A result that relates functors to categories
Question 6 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 neither a left nor right adjoint
Question 7 Multiple Choice (Single Answer)

What is a monad in category theory?

  1. A functor that maps a category to itself
  2. A functor that maps a category to a set
  3. A functor that maps a category to a category of functors
  4. A functor that maps a category to a category of categories
Question 8 Multiple Choice (Single Answer)

What is a limit in category theory?

  1. A construction that combines a family of objects into a single object
  2. A construction that combines a family of morphisms into a single morphism
  3. A construction that combines a family of categories into a single category
  4. A construction that combines a family of functors into a single functor
Question 9 Multiple Choice (Single Answer)

What is a colimit in category theory?

  1. A construction that combines a family of objects into a single object
  2. A construction that combines a family of morphisms into a single morphism
  3. A construction that combines a family of categories into a single category
  4. A construction that combines a family of functors into a single functor
Question 10 Multiple Choice (Single Answer)

What is the category of sets?

  1. The category whose objects are sets and whose morphisms are functions
  2. The category whose objects are categories and whose morphisms are functors
  3. The category whose objects are functors and whose morphisms are natural transformations
  4. The category whose objects are categories of functors and whose morphisms are functors between categories of functors
Question 11 Multiple Choice (Single Answer)

What is the category of categories?

  1. The category whose objects are categories and whose morphisms are functors
  2. The category whose objects are sets and whose morphisms are functions
  3. The category whose objects are functors and whose morphisms are natural transformations
  4. The category whose objects are categories of functors and whose morphisms are functors between categories of functors
Question 12 Multiple Choice (Single Answer)

What is the category of functors?

  1. The category whose objects are functors and whose morphisms are natural transformations
  2. The category whose objects are categories and whose morphisms are functors
  3. The category whose objects are sets and whose morphisms are functions
  4. The category whose objects are categories of functors and whose morphisms are functors between categories of functors
Question 13 Multiple Choice (Single Answer)

What is the category of categories of functors?

  1. The category whose objects are categories of functors and whose morphisms are functors between categories of functors
  2. The category whose objects are functors and whose morphisms are natural transformations
  3. The category whose objects are categories and whose morphisms are functors
  4. The category whose objects are sets and whose morphisms are functions
Question 14 Multiple Choice (Single Answer)

What is the Eilenberg-Steenrod axioms?

  1. A set of axioms that characterize the category of topological spaces
  2. A set of axioms that characterize the category of groups
  3. A set of axioms that characterize the category of rings
  4. A set of axioms that characterize the category of fields
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