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Category Theory and Topology

This quiz covers the fundamental concepts and principles of Category Theory and Topology, including categories, functors, natural transformations, topological spaces, and continuous maps.

15 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

In category theory, a functor is a mapping between:

  1. Categories and sets
  2. Categories and groups
  3. Categories and topological spaces
  4. Categories and functions
Question 2 Multiple Choice (Single Answer)

In topology, a topological space is defined as a set X together with:

  1. A collection of open sets
  2. A collection of closed sets
  3. A collection of compact sets
  4. A collection of connected sets
Question 3 Multiple Choice (Single Answer)

A continuous map between topological spaces is a function that:

  1. Preserves open sets
  2. Preserves closed sets
  3. Preserves compact sets
  4. Preserves connected sets
Question 4 Multiple Choice (Single Answer)

In category theory, a natural transformation between functors is a:

  1. Homomorphism
  2. Isomorphism
  3. Epimorphism
  4. Monomorphism
Question 5 Multiple Choice (Single Answer)

In topology, a compact space is a space that is:

  1. Closed and bounded
  2. Open and bounded
  3. Closed and unbounded
  4. Open and unbounded
Question 6 Multiple Choice (Single Answer)

In category theory, an isomorphism is a functor that is:

  1. Injective and surjective
  2. Injective but not surjective
  3. Surjective but not injective
  4. Neither injective nor surjective
Question 7 Multiple Choice (Single Answer)

In topology, a connected space is a space that:

  1. Cannot be separated into two disjoint open sets
  2. Can be separated into two disjoint open sets
  3. Is compact
  4. Is Hausdorff
Question 8 Multiple Choice (Single Answer)

In category theory, a category is a collection of:

  1. Objects and morphisms
  2. Objects and functions
  3. Morphisms and functions
  4. Objects and sets
Question 9 Multiple Choice (Single Answer)

In topology, a Hausdorff space is a space in which:

  1. Every point is closed
  2. Every point is open
  3. Every point has a unique neighborhood
  4. Every point is a limit point
Question 10 Multiple Choice (Single Answer)

In category theory, a monomorphism is a functor that is:

  1. Injective
  2. Surjective
  3. Bijective
  4. None of the above
Question 11 Multiple Choice (Single Answer)

In topology, a compact space is also known as a:

  1. Lindelöf space
  2. Hausdorff space
  3. Connected space
  4. Simply connected space
Question 12 Multiple Choice (Single Answer)

In category theory, an epimorphism is a functor that is:

  1. Injective
  2. Surjective
  3. Bijective
  4. None of the above
Question 13 Multiple Choice (Single Answer)

In topology, a connected space is also known as a:

  1. Path-connected space
  2. Simply connected space
  3. Locally connected space
  4. Arcwise connected space
Question 14 Multiple Choice (Single Answer)

In category theory, a category is said to be:

  1. Well-powered
  2. Small
  3. Large
  4. None of the above
Question 15 Multiple Choice (Single Answer)

In topology, a topological space is said to be:

  1. Regular
  2. Normal
  3. Hausdorff
  4. All of the above
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