Category Theory Illustrated - Functors

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2023-03-15 20:00:06

From this chapter on, we will change the tactic a bit (as I am sure you are tired of jumping through different subjects) and we will dive at full throttle into the world of categories, using the structures that we saw so far as context. This will allow us to generalize some of the concepts that we examined in these structures and thus make them valid for all categories.

We also learned about other algebraic objects that turned out to be just special types of categories, like categories that have just one object (monoids, groups) and categories that have only one morphism between any two objects (preorders, partial orders.)

We also defined a lot of categories based on different concepts, like the ones based on logics/programming languages, but also some “less-serious ones”, as for example the color-mixing partial order/category.

And most importantly, we saw some categories that are completely made up, such as my soccer player hierarchy. Those are formally called finite categories.

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