Lectures related to Categories

The Pigeonhole Principle: Basics and Applications

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

Isomorphism Criterion of Coverings

Covers the isomorphism of coverings and the lifting theory.

Relations in Computer Science

Explores the properties of relations in computer science, including equivalence relations and the partition of a set.

Set Theory: Operations and Functions

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

Limits and colimits: Two examples

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

Understanding Microcontrollers: Functions

Introduces the fundamentals of functions in microcontroller programming, emphasizing naming rules and step-by-step development.

Programming Fundamentals: Lists and Imports

Delves into Python lists, slicing, functions, and imports for code sharing.

Variables, Objects, Types

Introduces variables, objects, and types in Python, emphasizing the significance of object mutability and its implications when passing objects to functions.

Limits and Colimits: Equalizers and Coequalizers

Covers limits and colimits, focusing on equalizers and coequalizers in category theory.

Functions: Definitions and Notations

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

Definitions and Notations MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

Covers the definitions and notations related to functions.

Adjunctions and Limits: Exploring Functors and Co-limits

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

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Convexity Criteria MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Covers the study of functions, focusing on convexity criteria within closed subintervals.

Categories and Functors

Covers categories, functors, and presheaf categories, exploring the relationships between objects and morphisms.

Functions and Data

Covers the implementation of rational arithmetic using functions to encapsulate data structures.

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.

Differentiating under the integral sign

Explores differentiating under the integral sign and continuity of functions in integrals.

Real Functions: Definitions and Properties Log in to Mediaspace to watch this video

Explores real functions, covering parity, periodicity, and polynomial functions.

Functions and Periodicity Log in to Mediaspace to watch this video

Covers functions, including even and odd functions, periodicity, and function operations.