In mathematics, the free category or path category generated by a directed graph or quiver is the category that results from freely concatenating arrows together, whenever the target of one arrow is the source of the next. More precisely, the objects of the category are the vertices of the quiver, and the morphisms are paths between objects. Here, a path is defined as a finite sequence where is a vertex of the quiver, is an edge of the quiver, and n ranges over the non-negative integers. For every vertex of the quiver, there is an "empty path" which constitutes the identity morphisms of the category. The composition operation is concatenation of paths. Given paths their composition is . Note that the result of the composition starts with the right operand of the composition, and ends with its left operand. (Wikipedia).
From playlist Music.
Open Source vs. Closed Source Software
In this video, you’ll learn more about the differences between open-source software and closed-source software. Visit https://edu.gcfglobal.org/en/basic-computer-skills/ for more technology, software, and computer tips. We hope you enjoy!
From playlist Technology Trends
OpenStax illustrates the impact of a free book.
From playlist Exhibit Playlist
Vodafone-Happy to Help Ad (full)
In some very special way I still remain loyal to this brand,yet another spectaculary meaningful ad from O&M..gd going
From playlist Advertisements
DjangoCon US 2015 - Money, Money, Money... by Russell Keith-Magee
Money, Money, Money - Writing software, in a rich (wo)man's world Free software advocates talk about two types of "Free": Free as in freedom, and Free as in beer. While Free (as in freedom) software is unquestionably better for users and developers alike, Free (as in beer) software doesn'
From playlist DjangoCon 2015
It's here! Vote vote vote! Everyone can vote! I desperately need votes! Free Music (Beginnings) from: http://music4yourvids.co.uk/
From playlist BAGUETTE
Paul André Melliès - Dialogue Games and Logical Proofs in String Diagrams
After a short introduction to the functorial approach to logical proofs and programs initiated by Lambek in the late 1960s, based on the notion of free cartesian closed category, we will describe a recent convergence with the notion of ribbon category introduced in 1990 by Reshetikhin and
From playlist Combinatorics and Arithmetic for Physics: 02-03 December 2020
From playlist Open Q&A
Winter School JTP: Introduction to A-infinity structures, Bernhard Keller, Lecture 3
In this minicourse, we will present basic results on A-infinity algebras, their modules and their derived categories. We will start with two motivating problems from representation theory. Then we will briefly present the topological origin of A-infinity structures. We will then define and
From playlist Winter School on “Connections between representation Winter School on “Connections between representation theory and geometry"
Categories 5 Limits and colimits
This lecture is part of an online course on category theory. We define limits and colimits of functors, and show how various constructions (products, kernels, inverse limits, and so on) are special cases of this. We also describe how adoint functors preserve limits or colimits. For the
From playlist Categories for the idle mathematician
Type Systems I - Vladimir Voevodsky
Vladimir Voevodsky Institute for Advanced Study November 28, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Feynman categories, universal operations and master equations - Ralph Kaufmann
Ralph Kaufmann Purdue University; Member, School of Mathematics December 6, 2013 Feynman categories are a new universal categorical framework for generalizing operads, modular operads and twisted modular operads. The latter two appear prominently in Gromov-Witten theory and in string field
From playlist Mathematics
Christopher TOWNSEND - There are categories of ‘spaces' that are not categories of locales
Abstract We described a short list of categorical axioms that make a category behave like the category of locales. In summary the axioms assert that the category has an object that behaves like the Sierpnski space and this object is double exponentiable. A number of the usual results of lo
From playlist Topos à l'IHES
TOC 2011: Ben Lorica, "U.S. iTunes Appstore: Lessons from The First 30 Months"
In this talk Ben will go over a series of (surprising) observations backed by comprehensive data from the U.S. iTunes app store. He will present statistics and metrics that will help app sellers, marketers, and developers, understand recent dynamics in the U.S. app store. Along the way we'
From playlist TOC 2011
This lecture is part of an online course on category theory. We define adoint functors and give severalexamples of them. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj51F9XZ_Ka4bLnQoxTdMx0AL
From playlist Categories for the idle mathematician
Type Systems and Proof Assistant - Vladimir Voevodsky
Vladimir Voevodsky Professor, School of Mathematics, IAS October 10, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Lecture 12: Classifying topoi (Part 1)
This is the first of several talks on the subject of classifying topoi. I began with a brief reminder of the overall picture from the first talk, i.e. what are classifying topoi and why do we care (from the point of view of organising mathematics). Then I spent some time talking about tens
From playlist Topos theory seminar