Lectures related to Regularity Lemmas and Density Theorems

Covers propositions indexed by vectors, proof by induction, and Cartesian products of sets.

Covers the Pigeonhole Principle, its applications, and examples of its guarantees.

Explores homotopical algebra examples and adjunctions, focusing on left and right adjoints in group functors and coproducts.

Covers set theory operations and functions, including injections and surjections.

Covers the foundation of mathematics through set theory concepts like membership and unions.

Covers the construction of integers through equivalence relations and their properties in mathematics.

Covers adjunctions and limits, focusing on functors, co-limits, and their applications in category theory.