6TEKA Category Theory, winter semester 2023/2024
HOMEWORKS
Homework 5
Is it possible that a functor between two categories is simultaneously covariant
and contravariant?
Homework 7
Enumerate, up to isomorphism, all categories containing exactly 3 arrows, and
for each of them find all subcategories, up to isomorphism.
Homework 8
Recall that a constant functor between two categories \(\mathbb C\) and
\(\mathbb D\) is a functor sending each object of \(\mathbb C\) to a fixed
object \(A\) in \(\mathbb D\), and each arrow in \(\mathbb C\), to \(1_A\).
Describe all situations when a constant functor is isomorphism of categories.
Homework 10
Which of the three categories: \(\mathbb C_M\) for a fixed monoid \(M\),
\(\mathbb S_X\) for a fixed set \(X\), and \(\mathbf{Set}\) are equivalent?
Last modified: Tue Nov 5 2024 21:29:41 CET