In linguistics, an empty category, which may also be referred to as a covert category, is an element in the study of syntax that does not have any phonological content and is therefore unpronounced. Empty categories exist in contrast to overt categories which are pronounced. When representing empty categories in tree structures, linguists use a null symbol (∅) to depict the idea that there is a mental category at the level being represented, even if the word(s) are being left out of overt speech. The phenomenon was named and outlined by Noam Chomsky in his 1981 LGB framework, and serves to address apparent violations of locality of selection — there are different types of empty categories that each appear to account for locality violations in different environments. Empty categories are present in most of the world's languages, although different languages allow for different categories to be empty. (Wikipedia).
Empty Graph, Trivial Graph, and the Null Graph | Graph Theory
Whenever we talk about something that is defined by sets, it is important to consider the empty set and how it fits into the definition. In graph theory, empty sets in the definition of a particular graph can bring on three types/categories of graphs. The empty graphs, the trivial graph, a
From playlist Graph Theory
Why is the Empty Set a Subset of Every Set? | Set Theory, Subsets, Subset Definition
The empty set is a very cool and important part of set theory in mathematics. The empty set contains no elements and is denoted { } or with the empty set symbol ∅. As a result of the empty set having no elements is that it is a subset of every set. But why is that? We go over that in this
From playlist Set Theory
Empty Set vs Set Containing Empty Set | Set Theory
What's the difference between the empty set and the set containing the empty set? We'll look at {} vs {{}} in today's set theory video lesson, discuss their cardinalities, and look at their power sets. As we'll see, the power set of the empty set is our friend { {} }! The river runs peacef
From playlist Set Theory
We give a buttload of definitions for morphisms on various categories of complexes. The derived category of an abelian category is a category whose objects are cochain complexes and whose morphisms I describe in this video.
From playlist Derived Categories
Categories 6 Monoidal categories
This lecture is part of an online course on categories. We define strict monoidal categories, and then show how to relax the definition by introducing coherence conditions to define (non-strict) monoidal categories. We finish by defining symmetric monoidal categories and showing how super
From playlist Categories for the idle mathematician
Does space mean emptiness? How do you describe it?
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From playlist Science Unplugged: Physics
Category Theory 4.1: Terminal and initial objects
Terminal and initial objects
From playlist Category Theory
Category theory for JavaScript programmers #21: terminal and initial objects
http://jscategory.wordpress.com/source-code/
From playlist Category theory for JavaScript programmers
Serge Bouc: Correspondence functors
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
Category Theory 2.2: Monomorphisms, simple types
Monomorphisms, simple types.
From playlist Category Theory
Oscar Randal Williams: Moduli spaces of manifolds (part 3)
The lecture was held within the framework of the Hausdorff Trimester Program: Homotopy theory, manifolds, and field theories and Introductory School (05.05.2015)
From playlist HIM Lectures 2015
Duality In Higher Categories IV by Pranav Pandit
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)
Ilka Brunner - Truncated Affine Rozansky-Witten Models as Extended TQFTs
Mathematicians formulate fully extended d-dimensional TQFTs in terms of functors between a higher category of bordism and suitable target categories. Furthermore, the cobordism hypothesis identifies the basic building blocks of such TQFTs. In this talk, I will discuss Rozansky Witten model
From playlist Mikefest: A conference in honor of Michael Douglas' 60th birthday
Mark Balaguer - What Are the Things of Existence?
How many different kinds of 'things' are there? What are the fewest number of things that can characterize existence and do so exhaustively? In other words, what are the most basic building blocks of everything we see and know? From what things can all that exists be constructed? Are thing
From playlist Exploring Metaphysics - Closer To Truth - Core Topic
Math 101 Fall 2017 112917 Introduction to Compact Sets
Definition of an open cover. Definition of a compact set (in the real numbers). Examples and non-examples. Properties of compact sets: compact sets are bounded. Compact sets are closed. Closed subsets of compact sets are compact. Infinite subsets of compact sets have accumulation poi
From playlist Course 6: Introduction to Analysis (Fall 2017)
Jason Parker - Covariant Isotropy of Grothendieck Toposes
Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/ParkerSlidesToposesOnline.pdf Covariant isotropy can be regarded as providing an abstract notion of conjugation or i
From playlist Toposes online