Algebraic structures, encompassing groups, rings, fields and modules, have long formed the backbone of modern mathematics. Category theory, with its focus on objects and morphisms, provides a unifying ...

On a crisp fall New England day during my junior year of college, I was walking past a subway entrance when a math problem caught my eye. A man was standing near a few brainteasers he had scribbled on ...

The equal sign is the bedrock of mathematics. It seems to make an entirely fundamental and uncontroversial statement: These things are exactly the same. But there is ...

Semigroups, algebraic structures defined by a set equipped with an associative binary operation, are a cornerstone within modern algebra. Their study encompasses both abstract theoretical development ...

This is a preview. Log in through your library . Abstract The fields of algebra and representation theory contain abundant examples of functors on categories of modules over a ring. These include of ...

Mathematical truths are often born of the conflict between order and disorder. Mathematicians discover patterns, and, to better understand the mysterious forces at play, they look for countervailing ...

"Yoneda Theory for Double Categories" Theory and Applications of Categories, Vol. 25, No. 17, 2011, pp. 436–489. (With M. Grandis) "From cubical to globular higher categories" Diagrammes,supplément ...

Mathematician Cheng attempts to impart crucial life lessons via the fundamentals of math in her uneven latest (after Is Maths Real?). The focus is on the meaning of “sameness” and “difference” in both ...