A course in Category Theory.

Part 2: “Types of Morphisms.”

Join Medium with my referral link - applied.math.coding

This story belongs to a series that has started here.

We are going now into looking at different features morphisms can have. As typical for category theory, the concepts are carried over from the category of sets into a more abstract formulation.

First let us have a look how the set-theoretic properties surjective and injective can be formulated by only using functions. This allows us later to abstract these properties into a category theoretic formulation.

So for now we are in the category of sets:

(in case the embedded PDF renders blank, you can use this link)

Next, we leave the specific category of sets and will use the above reformulation of injectivity and surjectivity to define suitable abstractions in terms…