/explore
|
You are here 
|
blog.ploeh.dk | ||
| | | | |
www.jeremykun.com
Last time we worked through some basic examples of universal properties, specifically singling out quotients, products, and coproducts. There are many many more universal properties that we will mention as we encounter them, but there is one crucial topic in category theory that we have only hinted at: functoriality. As we've repeatedly stressed, the meat of category theory is in the morphisms. One natural question one might ask is, what notion of morphism is there between categories themselves? |
|
| | | | | ||
| | | | |
bartoszmilewski.com
Previously: Kan Extensions in Double Categories. In programming, actegories play a central role in optics: lenses, prisms, traversals, etc. To understand actegories, let's start with the definition of a monoidal category. Monoidal Category A monoidal category $latex \mathbf M$ is a category equipped with a tensor product. A tensor product is a functor $latex \otimes... |
|
| | | | | ||
| | | | |
bartoszmilewski.com
This is part of Categories for Programmers. Previously: Simple Algebraic Data Types. See the Table of Contents. At the risk of sounding like a broken record, I will say this about functors: A functor is a very simple but powerful idea. Category theory is just full of those simple but powerful ideas. A functor is... |
|
| | | | | ||
| | | | |
www.jeremykun.com
A lot of people who like functional programming often give the reason that the functional style is simply more elegant than the imperative style. When compelled or inspired to explain (as I did in my old post, How I Learned to Love Functional Programming), they often point to the three "higher-order" functions map, fold, and filter, as providing a unifying framework for writing and reasoning about programs. But how unifying are they, really? |
|
| | | |||
