Monads Category Theory by Example
Monads arise from monoids in the category of endofunctors and model structured computation in programming languages.
Archive
2019
Objects and Morphisms Category Theory by Example
Universal constructions describe initial and terminal objects, products, sums, monoids, exponential objects, and type algebra.
Notes on strict weak ordering and why violating std::sort comparator requirements can corrupt results.
Introduction Category Theory by Example
The series introduces category theory as a connected collection of definitions, examples, and applications in sets, programming languages, and physics.
Abstract Algebra Category Theory by Example
Groups, rings, fields, and vector spaces provide algebraic background used by the categorical examples.
A quantum teleportation protocol based on entangled photon pairs and Bell-state measurement, followed by the Mermin-Peres pseudo-telepathy game as a second application of entanglement.
Topos Category Theory by Example
Topos theory studies categories that behave like generalized universes of sets.
Yoneda's Lemma Category Theory by Example
Yoneda's lemma explains how an object of a locally small category is determined by the morphisms into or out of it.
Natural Transformations Category Theory by Example
Natural transformations compare functors component by component and organize functors into their own categories.
Functors Category Theory by Example
Functors map objects and morphisms between categories while preserving composition and identity.