Lectures related to Commutative diagram

Covers the Algebraic Kunneth Theorem, explaining chain complexes and cohomology computations.

Covers the properties of vectors, including commutativity, distributivity, and linearity.

Covers associative and commutative operations in parallel programming, using mathematical examples and discussing challenges in preserving associativity.

Commutativity in Rings

Covers commutativity in rings, evaluation options, and formal linear combinations.

Quotients de groupe: Un cas particulier

Explores a categorical perspective on group quotients, focusing on a specific case.

The Topological Künneth Theorem

Explores the topological Künneth Theorem, emphasizing commutativity and homotopy equivalence in chain complexes.

Set Union: Properties and Operations

Explains the union of sets, its properties, operations, and intersection.

Construction of Free Action Functor

Explores the construction of the free action functor and its equivariance.

Auxiliary Assertions in Stainless

Showcases the use of assertions in Stainless to prove properties of fractions.

Elliptic Curves: Group Structure and Isomorphism

Explores the group structure and isomorphism of elliptic curves, including inverses, associativity, and compactification to the torus.

Natural Transformations: Definition

Covers the definition and properties of natural transformations between functors in category theory.

Proof of Existence

Explores morphisms in group theory, focusing on proving their existence and uniqueness through mathematical reasoning.

Intersection: Set Operations

Introduces set intersection, its properties, and its relation to arithmetic operations.

Simplicial and Singular Homology Equivalence

Demonstrates the equivalence between simplicial and singular homology, proving isomorphisms for finite s-complexes and discussing long exact sequences.

The Lemma of the Five: Abelian Groups

Presents the Lemma of the Five, a fundamental result in group theory.

Natural Transformations in Group Theory

Introduces natural transformations in group theory and category theory, emphasizing their definition and significance.

Zig Zag Lemma

Covers the Zig Zag Lemma and the long exact sequence of relative homology.

Electromagnetic Problems: Well-Posedness and Convergence

Explores the well-posedness and convergence of electromagnetic problems, including continuity interpolation, Darcy's law, and surjectivity properties.

Cofibrations: Extension Property and Recognition Principle

Explores the extension property of spaces and the recognition principle for cofibrations.

Natural Numbers: Properties and Operations

Explores natural numbers, their properties, operations, and practical applications like calculating hours in a year.