Fernando Cejas
May 05, 2022
160

Just a tiny presentation trying to explain monadic types in 10 minutes by giving a bit of an overview of Mathematics Category Theory.

May 05, 2022

## Transcript

In 10 minutes…???

2. — Someone not Famous
“The goal of Category theory is to show
that trivial things are trivially trivial…”

Category Theory
01

4. Category Theory is a mathematical discipline with a wide range of
applications in theoretical computer science. Concepts like Category, Functor,
Monad, and others, which were originally deﬁned in Category Theory, have
become pivotal for the understanding of modern Functional Programming (FP)
The meaning and applications of these terms in FP can be understood without
in-depth knowledge of the corresponding mathematical deﬁnitions and
axiomatic. However, a common knowledge of the underlying theory can help
FP programmers understand the design and structure of commonly used
libraries and tools and be more productive.
Category Theory

5. Whoa!
● Categories
● Monoids
● Isomorphisms
● Duality Principle
● Functors
Shamelessly taken from wikibooks of haskell
functions as morphisms and uses for composition ((\circ)) the
function ((.)), a function (f :: A -> B) for types A and B is a

6. Categories
Map of the Middle Earth of the Lord of the Rings. Elves have made it.

7. Functors
Now another map of the Seven Kingdoms of Game of Thrones.

8. Functors… and transform
01
02
03
04

9. Whoa!

Now another map of the Middle Earth, but this time, drawn by a Dwarf.

If an endofunctor also fulﬁlls that it has two natural transformations such as
the identity function and another function that is associative, we can say that

From a Functional Programming perspective…

encapsulates a computation
that supports 2 main functions:
map()
ﬂatMap()

14. Tiny
demo
We are not fully aware on how