Warning. Failure of sum isomorphisms [dt-003C]

Liam O'Connor

The weakness of the universal property for sums means that many common isomorphisms for sums in other contexts do not hold:

$A + (B + C) \not \simeq (A + B) + C$
$(A \twoheadrightarrow C) \times (B \twoheadrightarrow C) \not \simeq (A+B) \twoheadrightarrow C$