Three years ago I thought it would be fun to write a blog post every day of November. I’m not sure why I didn’t do this in November 2010 or 2011 because I’m pretty sure I learned a lot from doing it in 2009, so I’d like to do it again. The posts will probably be shorter this time.
Archive for October, 2012
There are various natural questions one can ask about monomorphisms and epimorphisms all of which lead to the same answer:
- What is the “easiest way” a morphism can be a monomorphism (resp. epimorphism)?
- What are the absolute monomorphisms (resp. epimorphisms) – that is, the ones which are preserved by every functor?
- A morphism which is both a monomorphism and an epimorphism is not necessarily an isomorphism. Can we replace either “monomorphism” or “epimorphism” by some other notion to repair this?
- If we wanted to generalize surjective functions, why didn’t we define an epimorphism to be a map which is surjective on generalized points?