Skip to content

Products, sums, and their morphisms

Genady
in Linear Algebra and Group Theory

Featured Replies

Check this exercise:

image.png

I think, the text is mistaken. In the category of sets, a direct product of A and B is their Cartesian product C, and the morphisms are maps from C to A and from C to B, which are not injective, i.e., monomorphisms, but rather surjective, i.e., epimorphisms.

OTOH, a direct sum of sets A and B is their disjoint union C, and the morphisms are maps from A to C and from B to C, which are not surjective (epimorphisms), but rather injective (monomorphisms).

Do you agree?

Create an account or sign in to comment
Go to topic listing

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.

Account

Navigation

Search

Search

Configure browser push notifications
Chrome (Android)
  1. Tap the lock icon next to the address bar.
  2. Tap Permissions → Notifications.
  3. Adjust your preference.
Chrome (Desktop)
  1. Click the padlock icon in the address bar.
  2. Select Site settings.
  3. Find Notifications and adjust your preference.