Bartoszmilewski.com

Consider the humble Applicative. More than a functor, less than a monad. It gives us such lovely syntax. Who among us still prefers to write liftM2 foo a b when we could instead write foo a b? But we seldom use the Applicative as such — when Functor...

Applicative functors are well-known and well-loved among Haskellers, for their ability to apply functions in an effectful context. In category-theoretic terms, it can be shown that the methods of Applicative: are equivalent to having a Functor f with...

My grad students and I have been using a lot of category theory in our work on networks in engineering, chemistry and biology. So, I decided to teach an introductory course on category theory, and it was surprisingly popular: 25 grad students registered...

This has been dragging forever. Let me cover it, shedding light to the dark corners, ok? Introduction First, definitions. I'll try to use, as much as possible, Scala notation, and, basically, Scala terms. A category consists of types and functions...

Let $\mathcal{V_1}$ and $\mathcal{V_2}$ be cocomplete symmetric monoidal categories, each endowed with a cosimplicial object $\Delta^\bullet=\Delta^\bullet_{\mathcal{V}_i}:\Delta \to \mathcal{V}_i$. Denote by $|-|=|-|_{\mathcal{V}_i}:s\mathcal{V}_i\to...