Lectures related to Functor | EPFL Graph Search

Categories and Functors: An Introduction

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

Explores natural transformations in algebra, defining functors and isomorphisms.

Natural Transformations: Functors and Categories

Explores functors, natural transformations, and the theory of groups, emphasizing the importance of comparisons and structure preservation.

Natural Transformations

Explores natural transformations between functors, emphasizing their composition-preserving properties and significance in category theory.

Natural Transformations: Examples and Applications

Explores natural transformations between functors in different categories and their applications.

Functor Categories Composition and Induced Functors

Explores composition of functors, induced functors, and preservation of commutative diagrams in category theory.

Homotopical Algebra: Examples and Adjunctions

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

Categories and Functors

Explores building categories from graphs and the encoding of information by functors.

Introduction to Category Theory: Functors

Covers the concept of functors in category theory, including composition, identity functors, and forgotten functors.

Group Actions: Equivariance and Functors

Explores equivariance in group actions and functors, demonstrating its importance in group theory.

Divisibility and Torsion

Explores divisibility and torsion in group theory, focusing on defining a functor that preserves divisibility.

Group Actions: G-objects in a Concrete Category

Explores G-objects in a concrete category and the framework for group actions.

Active Learning Session

Explores natural transformations in group theory and category theory, emphasizing functor composition and morphism composition.

Categorical Context of G-objects

Delves into the categorical framework for group actions and the correspondence between G-actions on c and functors from BG to C.

Natural Transformations: Examples

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

Introduction to Category Theory: Natural Transformations

Covers the concept of natural transformations between functors and their associativity.

Group Theory: Adjoint Functors and G-sets

Explores adjunction between functors, composition of applications, G-equivariance, and natural transformations in G-sets.

Functors: Assigning Morphisms and Dual Spaces

Covers the concept of functors, assigning morphisms and dual spaces in different categories.

Introduction to Category Theory: Adjoint Functors

Introduces adjoint functors in category theory, emphasizing their significance and applications in establishing relationships between different categories.

Limits and colimits: Concrete Examples

Explores concrete examples of limits and colimits in functors and different categories.