A course in Category Theory.

applied.math.coding
2 min readOct 25, 2021

Part 2: “Types of Morphisms.”

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 of general categories:

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

We will see that these abstractions only under specific conditions behave the same like their set-theoretic counterpart. But before we proceed, let us hold on considering a few examples. For the first example it might be helpful but not necessary to recall the category ‘Mon’ that you may find in the example section of here.

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

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applied.math.coding

I am a Software Developer - Rust, Java, Python, TypeScript, SQL - with strong interest doing research in pure and applied Mathematics.