# Curry-Howard-Lambek Isomorphism

$\boxed {\text {Category} \iff \text {Algebra} \iff \text {Logic} \iff \lambda \text {-Calculus}}$

Below the lecturer said every aspect of Math can be folded out from Category Theory, then why not start teaching Category Theory in schools.

That was the idea proposed by Alexander Grothendieck to the Bourbakian Mathematicians who rewrote all Math textbooks after WW2, instead of in Set Theory, should switch to Category Theory. His idea was turned down by André Weil.

$\boxed { a^{b + c} = a^{b} \times a^{c} }$

$\boxed {\text {Left-side: Either b c } \to a}$

$\boxed {\text {Right-side: } (b \to a , c\to a) }$

$\boxed { (a^{b})^{c} = a^{b \times c}}$

$\boxed { c \to (b \to a) \sim (b ,c) \to a}$

$\boxed { (a \times b)^{c} = a^{c} \times b^{c}}$

$\boxed {c \to (a,b) \sim (c \to a , c \to b)}$