Concept

Category of sets

Related lectures (29)

Sets and Operations: Introduction to Mathematics

Covers the basics of sets and operations in mathematics, from set properties to advanced operations.

Covers the generalities of functions, including the definition of an application between sets and the uniqueness of elements in the image set.

Cartesian Product and Induction

Introduces Cartesian product and induction for proofs using integers and sets.

Linear Algebra: Sets and Operations

Introduces fundamental concepts of linear algebra, focusing on sets and operations.

Group Actions and Functors

Covers group quotient, group actions, and functors connecting sets and G-sets.

Limits and Colimits: Understanding Categories

Explores limits and colimits in category theory, discussing their definitions, properties, and applications, including the non-existence of limits in certain categories and the relationships between limits and colimits under functors.

Sets and Proofs

Introduces sets in discrete mathematics and explores proof techniques like direct and indirect proofs.

Linear Algebra: Bijections and Cardinality

Explores bijections in linear algebra and the concept of cardinality between sets.

Concrete Categories

Covers concrete categories with sets and structures, including Ens, Gr, Ab, and Vectk.

Categorical Perspective: Group Actions

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

Sets, Functions and Relations: Quiz

Covers subsets, power sets, and functions through an engaging quiz format.

Homotopy Theory of Chain Complexes

Explores the homotopy theory of chain complexes, focusing on model categories, weak equivalences, and the retraction axiom.

Limits and colimits: Two examples

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

Products: Theory of Categories

Covers the concept of products in category theory, focusing on their properties, uniqueness, and isomorphisms.

Introduction to Coproducts

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

Exam Information

Covers details of the upcoming theoretical exam, including structure and guidelines.

Abbreviated Calculation: Structures and Sets

Covers abbreviated calculation, structures, operations, and unique set properties.

Category Theory: Introduction

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

Relations: Composition and Reciprocal

Introduces the concept of relations, composition, and reciprocity between sets.

Combinatorial Search Example

Covers sets in Scala, N-Queens problem, and recursive algorithms.