6TEKA/7TEKA/TEKAT Category Theory, winter semester 2020/2021

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?


Created: Fri Oct 23 2020
Last modified: Thu Nov 28 2024 21:59:08 CET