Lectures related to Products: Theory of Categories

Introduces coproducts in category theory, exploring their properties, universality, and relationships with products.

Explores coproducts, universal properties, and natural transformations in category theory.

Explores group quotients and push-outs, discussing isomorphisms and surjectivity in different scenarios.

Lifting Properties in Model Categories: An Overview

Provides an overview of lifting properties in model categories, focusing on their definitions and implications for morphisms and commutative diagrams.

Category Theory: Introduction

Covers the basics of categories and functors, exploring properties, composition, and uniqueness in category theory.

Limits and colimits: Two examples

Focuses on the pushout and pullback constructions in sets, illustrating colimits and limits with explicit examples.

Limits and colimits: Introduction, Chapter 1(c)

Introduces limits and colimits in a category, covering their properties and uniqueness.

Adjunctions and Limits: Exploring Functors and Co-limits

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

Natural Transformations: Definition

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

Categorical Perspective: Group Actions

Generalizes group actions beyond sets, providing a comprehensive framework for various mathematical contexts.

Active Learning in Category Theory

Explores examples of categories, morphisms, groupoids, and functors in category theory.

Pushouts in Group Theory: Universal Properties Explained

Covers the construction and universal properties of pushouts in group theory.

Introduction to Categories: Products and Coproducts

Introduces the theory of categories by generalizing the Cartesian product and disjoint union of sets to any category.

Active Learning Session

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

Group Theory: Restriction Functor

Explores the restriction functor in group theory, focusing on its properties.

Functors: Definition

Introduces functors in category theory and explains their composition.

Introduction to Category Theory: Examples

Introduces the theory of categories through examples and discusses the product of categories.

Mutually Inverse Alpha and Beta

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

Lifting properties, Chapter 2(a): Definition and elementary properties of model categories

Covers morphisms with lifting properties, pushouts, pullbacks, and the uniqueness in the universal property of pushouts.

Left Adjoint Preserves Coproducts

Explores how left adjoints preserve coproducts in category theory with detailed proofs and morphism diagrams.