In this video we state and prove the Yoneda Lemma, and give examples of it in action within the category of graphs and the category of dynamical systems. There is also speculation about possible relations between the Yoneda Lemma and notions from particle physics and philosophical ideas about the (potentially) fractal nature of reality, like Indra's Necklace.
I have been working through Colin McLarty's book `Elementary Categories, Elementary Toposes'. I have been making rough videos on the different chapters and exercises. These provide an informative and laconic course on category theory (although the videos are unedited and rough). I provide links to these unlisted videos below (and will update the list as I work through more of the book). The videos are in the proper order.
McLarty Basics 1
• McLarty Basics 1
Basics Ex 1
• Basics Ex 1
Products 1
• Products 1
Products 2
• Products 2
Products Ex
• Products ex
Subobjects and pullbacks 1
• Subobjects and pullbac...
Subobjects and pullbacks 2
• Subobjects and pullbac...
Pullback Lemma 1
• Pullback Lemma 1
Pullback Lemma 2
• Pullback Lemma 2
Pullback Lemma 3
• Pullback Lemma 3
Pullback Lemma 4
• Pullback Lemma 4 example
Pullback Lemma 5
• Pullback Lemma 5
Pullback Lemma 6
• Pullback Lemma 6
Limits via equalizers 1
• Limits via equalizers 1
Limits via equalizers 2
• Limits via equalizers 2
Pullback exercises 1
• Pullback exercises 1
Pullback exercises 2
• Pullback exercises 2
Relations 1
• Relations 1
Relations 2
• Relations 2
Exponential objects 1
• Exponential Objects 1
Exponential objects 2
• Exponential objects 2
Exponential objects 3
• Exponential objects 3
Exponential objects 4
• Exponential objects 4
Exponential objects 5
• Exponential objects 5
Exponential objects 6
• Exponential objects 6
Exponential objects 7
• Exponential objects 7
Exponential objects 8
• Exponential objects 8
Exponential objects 9
• Exponential objects 9
Exponential objects 10
• Exponential objects 10
Mclarty Topos Basics 1
• Mclarty Topos Basics 1
Mclarty Topos Basics 2
• Mclarty Topos Basics 2
Mclarty Topos Basics 3
• Mclarty Topos Basics 3
Mclarty Topos Basics 4
• Maclarty Topos Basics 4
Mitchell-Benabou Language 1
• Mitchell-Benabou Langu...
Mitchell-Benabou Language 2
• Mitchell-Benabou Langu...
Mitchell-Benabou Language 3
• Mitchell-Benabou Langu...
Mitchell-Benabou Language 4
• Mitchell-Benabou Langu...
Mitchell-Benabou Language 5
• Mitchell-Benabou Langu...
Mitchell-Benabou Language Redone 1
• Mitchell-Benabou Langu...
Mitchell-Benabou Language Redone 2
• Mitchell-Benabou Langu...
Mitchell-Benabou Language Redone 3
• Mitchell-Benabou Langu...
Mitchell-Benabou Language Redone 4
• Mitchell-Benabou Langu...
Mitchell-Benabou Language Redone 5
• Mitchell-Benabou Langu...
Mitchell-Benabou Language Redone 6
• Mitchell-Benabou Langu...
Mitchell-Benabou Language Redone 7
• Mitchell-Benabou Langu...
Mitchell-Benabou Language Redone 8
• Mitchell-Benabou Langu...
Subobjects of exponential objects
• Subobjects of exponent...
Understanding exponential objects
• Understanding exponent...
Understanding exponential objects 2
• Understanding exponent...
Epimorphisms in MBL
• Epimorphisms in Mitche...
Existential quantifier interpretation
• Existential quantifier...
Universal quantifier in MBL 1
• Universal quantificati...
Universal quantifier in MBL 2
• Universal quantificati...
Universal quantifier in MBL 3
• Universal quantificati...
Universal quantifier in MBL 4
• Universal quantificati...
MBL implies rule
• MBL implies rule
MBL thinning, cut etc.
• MBL rules for And, Cut...
MBL rules, singleton, equality etc.
• MBL proofs for singlet...
MBL extensionality 1
• MBL extensionality 1
MBL extensionality 2
• MBL extensionality 2
MBL comprehension
• MBL comprehension
MBL substitution lemma
• MBL Substitution Lemma
MBL false not or
• MBL false, not, or
MBL false not or 2
• MBL false not or 2
MBL exists derivation
• MBL exists derivation
Kripke-Joyal Semantics Intro
• Kirpke-Joyal semantics...
Singleton arrows
• Singleton arrows
Kirpke-Joyal implies rule
• Kirpke-Joyal implies rule
Functional relations 1
• Functional relations 1
Functional relations 2
• Functional relations 2
Forall and exists in Set
• Forall and exists in Set
Functional relations 3
• Functional relations 3
The rest of the videos in this series are linked to within the description of my video: Category Theory For Beginners: Adjoint Functors
My own accompanying notes can be found here:
drive.google.c...
8 сен 2024
