#mathematics

An introductory overview of how category theory concepts can be applied to artificial intelligence.

This series delves into the intersection of category theory and artificial intelligence, providing insights into how abstract mathematical concepts can inform and enhance the design of AI systems. Each part builds on the previous one, so st...

A worked path through Seely's 2-categorical lambda calculus: from one term with two beta reductions to interchange, laxity, and the adjunction between currying and uncurrying.

Fix a type $O$, a closed function $f:O\Rightarrow O$, and one free input $y:O$. Consider the term $$ T(y) = (\lambda u:O.\,u) \big((\lambda v:O.\,v)(f\,y)\big). $$ It contains two beta redexes. We can contract the outer one first, $$ T(y) \...