Why are operads useful?

Why are operads useful?

The question is not about where operads are used, I know that. It is about what makes them useful. For example, van Kampen diagrams are useful in combinatorial group theory because these are planar

What is an Operad? Part 1

If you browse through the research of your local algebraist, homotopy theorist, algebraic topologist or―well, anyone whose research involves an operation of some type, you might come across the word "operad." But what are operads? And what are they good for? Loosely speaking, operads―which come in a wide variety of types―keep track of various "flavors" of operations.

Operads, Type Level Nats, and Tic-Tac-Toe

This summer I spent some time talking with Edward Kmett about lots of things. (Which really means that he was talking and I was trying to keep up.) One of the topics was operads. The ideas behind o…

Opera Neon. This browser is built to act.

Opera Neon is an agentic browser that understands your intent, assists with tasks, and takes actions. It helps you move faster and get things done.

The operad of wiring diagrams: formalizing a graphical language for databases, recursion, and plug-and-play circuits

Wiring diagrams, as seen in digital circuits, can be nested hierarchically and thus have an aspect of self-similarity. We show that wiring diagrams form the morphisms of an operad $\mcT$, capturing this self-similarity. We discuss the algebra $\Rel$ of mathematical relations on $\mcT$, and in so doing use wiring diagrams as a graphical language with which to structure queries on relational databases. We give the example of circuit diagrams as a special case. We move on to show how plug-and-play devices and also recursion can be formulated in the operadic framework as well. Throughout we include many examples and figures.

Opera unveils an AI agent that runs natively within the browser | TechCrunch

Browser company Opera has unveiled a new AI agent called Browser Operator that can complete tasks for you on different websites. In a demo video, the

Generalized Lens Categories via functors $\mathcal{C}^{\rm op}\to\mathsf{Cat}$

Lenses have a rich history and have recently received a great deal of attention from applied category theorists. We generalize the notion of lens by defining a category $\mathsf{Lens}_F$ for any category $\mathcal{C}$ and functor $F\colon \mathcal{C}^{\rm op}\to\mathsf{Cat}$, using a variant of the Grothendieck construction. All of the mathematics in this note is straightforward; the purpose is simply to see lenses in a broader context where some closely-related examples, such as ringed spaces and open continuous dynamical systems, can be included.

Seven Sketches in Compositionality: An Invitation to Applied Category Theory

This book is an invitation to discover advanced topics in category theory through concrete, real-world examples. It aims to give a tour: a gentle, quick introduction to guide later exploration. The tour takes place over seven sketches, each pairing an evocative application, such as databases, electric circuits, or dynamical systems, with the exploration of a categorical structure, such as adjoint functors, enriched categories, or toposes. No prior knowledge of category theory is assumed. A feedback form for typos, comments, questions, and suggestions is available here: https://docs.google.com/document/d/160G9OFcP5DWT8Stn7TxdVx83DJnnf7d5GML0_FOD5Wg/edit

Introduction

What the Pentaract is and why does exists.

Tiling Is the Missing Abstraction in Graphics Programming

A software engineer’s playbook for tiling: scheduling, threadgroups, and the small decisions that make performance predictable.

ravarcheon

mostly music, art, some math, a bit of code, webstuff, girlstuff, etc

A Very Early History of Algebraic Data Types

Been quiet around here! I’ve been putting almost all of my writing time into Logic for Programmers and my whole brain is book-shaped. Trust me, you do not want to read my 2000-word rant on Sphinx post-build LaTeX customization. But I spent the past week in a historical rabbit hole and had to share what I found. It started with Algebraic [Data] Types are not Scary, Actually. The post covers AlgDTs1 in more detail, but a quick overview is:

Category Theory Illustrated - index

What does a debate between two ancient Greek philosophers have to do with the code running your computer? How can a simple map reveal the deepest secrets of the universe’s structure?

Opera Mini is a game change : Cloud-Based Browsers and Its important to know them.

Index Introduction