• Functors – Exercise 1

    Show that functors preserve isomorphism. If $$a\sim a’$$ in $$\mathcal{C}$$, then $$F(a)\sim F(a’)$$ in $$\mathcal{H}$$, with $$F:\mathcal{C}\longrightarrow\mathcal{H}$$. Solution: Let $$f:a\longrightarrow a’$$ be a isomorphism with...

  • Categories – Exercise 1

    [Two-out-of-three property]  Let f: A→B and g: B→ C be two morphisms. If $$g$$ and $$gf$$ are isomorphisms, then so is f$$. Solution: There exists...