Lectures related to Monad (category theory)

Explores monads, their laws, Scala implementation, and practical applications in functional programming.

Covers the concepts of limits and colimits in the category of Topological Spaces, emphasizing the relationship between colimit and limit constructions and adjunctions.

Simplicial and Cosimplicial Objects: Examples and Applications

Covers simplicial and cosimplicial objects in category theory with practical examples.

Active Learning Session: Group Theory

Explores active learning in Group Theory, focusing on products, coproducts, adjunctions, and natural transformations.

Adjunctions and Functor Categories: Exploring Connections

Covers adjunctions and functor categories, emphasizing their significance in category theory and applications in deep learning.

Homotopical Algebra: Functor and Adjunctions

Delves into homotopical algebra, defining functors and adjunctions with examples.

Homotopical Algebra: Examples and Adjunctions

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

Adjunctions and Limits: Exploring Functors and Co-limits

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

Categories and Functors: An Introduction

Provides an overview of categories, functors, and natural transformations in mathematics.

Examples, Chapter 1(b): Adjunctions

Presents concrete examples of adjunctions between Set and Top categories.

Fixed Points and Orbits Analysis: Group Actions

Explores the definition of orbits and fixed points of a G-object in any category, focusing on G-equivariant applications.

Triangular Identities

Covers triangular identities, natural transformations, commutative diagrams, and adjunction notation in group and category theory.

Mutually Inverse Alpha and Beta

Explores adjunctions and mutual inverses alpha and beta in category theory.

Second Triangular Identity

Explores the second triangular identity in category theory and its applications in mathematical scenarios.

Functors and Adjunctions

Explores functors between categories and the conditions for left and right adjoints.

Natural Transformations: Examples

Introduces natural transformations through examples, covering equivalence of categories and functor properties.

Equivalences de Catégories et Adjonctions

Explores category equivalences, adjunctions, and group actions in category theory.

Natural Transformations: Adjunctions and Triangular Identities

Explores adjunctions, triangular identities, and natural transformations in category theory.

Introduction to Category Theory: Adjoint Functors

Explores a concrete example of adjunction in category theory and covers natural transformations and group theory concepts.

Free Abelian Groups: Group Theory

Explores the concept of free abelian groups as an important left adjoint functor.