Lectures related to Categories

The Pigeonhole Principle: Basics and Applications

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

Real Functions: Definitions and Properties

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

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.

Functions and Periodicity

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

Limits and colimits: Two examples

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

Euclidean Spaces: Properties and Concepts

Covers the properties of Euclidean spaces, focusing on R^n and its applications in analysis.

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.

Partial Derivatives: Definitions and Examples

Covers the concept of partial derivatives and their applications in mathematical analysis.

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.

Entropy and the Second Law of Thermodynamics

Covers entropy, its definition, and its implications in thermodynamics.

Definitions and Notations

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.

Open Balls and Topology in Euclidean Spaces

Covers open balls in Euclidean spaces, their properties, and their significance in topology.

Differential Forms on Manifolds

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

Convexity Criteria

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