HOMEWORKS
Homework 10 (2 points).
Prove that the map from \(\mathbf{Group}\) to itself, sending a group to its
commutator, cannot be made a functor.
The statement to prove was wrong: the map sending a group to
its commutator, is a functor!
Homework 11 (0.5 points).
Give an example of a category which is isomorphic to its own opposite.
Homework 13 (1 point).
Is it true that for any two monoids \(M\) and \(N\), the categories
\(\mathbf{C}_M\) and \(\mathbf{C}_N\) are equivalent if and only if they are
isomorphic?
Homework 14 (1 point).
Whether there exist two equivalent categories, one of which is small, and
another is large?
Homework 16 (1 point).
What will be the adjoint functor to the functor
\(\mathbf{Set} \to \mathbf{Top}\), assigning to each set the topological space
on this set with the trivial topology?
Created: Fri Oct 23 2020
Last modified: Thu Dec 09 19:26:10 Central Europe Standard Time 2021