HoTT Math

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34 videos

HoTT Math offers a step-by-step exploration of foundational mathematics. Using Homotopy Type Theory, we examine types, propositions, and proofs with rigour a...

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#33 Homotopy Type Theory Explained Higher Dimensional Loop Spaces, Abelian Groups

#32 Homotopy Type Theory Explained Suspensions

#31 Homotopy Type Theory Explained Function Extensionality

#30 Homotopy Type Theory Explained Pullbacks, Pushouts

#29 Homotopy Type Theory Explained Quotient Groups

#28 Homotopy Type Theory Explained Group Homomorphisms

#27 Homotopy Type Theory Explained Free products, Wedge sums

#26 Homotopy Type Theory Explained Covering Spaces

#25 Homotopy Type Theory Explained Univalence Axiom

#24 Homotopy Type Theory Explained Equivalences, Preimages

#23 Homotopy Type Theory Explained Groups, Truncations, Loop Spaces, Integers

#22 Homotopy Type Theory Explained Monoids, Sets, Mere Propositions

#21 Homotopy Type Theory Explained Contractibility, Interval Type

#20 Homotopy Type Theory Explained Sections

#19 Homotopy Type Theory Explained Mapping out of S¹, Functoriality

#18 Homotopy Type Theory Explained Path-lifting

#17 Homotopy Type Theory Explained Fibrations, Transport

#16 Homotopy Type Theory Explained Torus, Transitivity of equality

#15 Homotopy Type Theory Explained Higher Inductive Types, Circle, Sphere

#14 Homotopy Type Theory Explained Inductors

#13 Homotopy Type Theory Explained Recursors, Multiplication, Factorial

#12 Homotopy Type Theory Explained Addition, Currying, Functions from Inductive Types

#11 Homotopy Type Theory Explained Inductive Types, Finite Sets, Natural Numbers

#10 Homotopy Type Theory Explained Path Induction

#9 Homotopy Type Theory Explained Law of Excluded Middle, Lambda Calculus

#8 Homotopy Type Theory Explained Existential Quantifiers

#7 Homotopy Type Theory Explained Σ-types

#6 Homotopy Type Theory Explained Coproducts

#5 Homotopy Type Theory Explained Products

#4 Homotopy Type Theory Explained Universal Quantifiers