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Concept

Monad (category theory)

Related lectures (32)

Monads: Concepts and Applications

Explores monads, their laws, Scala implementation, and practical applications in functional programming.

Limits and colimits in Top

Covers the concepts of limits and colimits in the category of Topological Spaces, emphasizing the relationship between colimit and limit constructions and adjunctions.

Simplicial and Cosimplicial Objects: Examples and Applications

Covers simplicial and cosimplicial objects in category theory with practical examples.

Adjunctions and Functor Categories: Exploring Connections

Covers adjunctions and functor categories, emphasizing their significance in category theory and applications in deep learning.

Adjunctions and Limits: Exploring Functors and Co-limits

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

Categories and Functors: An Introduction

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

Examples, Chapter 1(b): Adjunctions

Presents concrete examples of adjunctions between Set and Top categories.

Triangular Identities

Covers triangular identities, natural transformations, commutative diagrams, and adjunction notation in group and category theory.

Mutually Inverse Alpha and Beta

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

Second Triangular Identity

Explores the second triangular identity in category theory and its applications in mathematical scenarios.

Functors and Adjunctions

Explores functors between categories and the conditions for left and right adjoints.

Natural Transformations: Examples

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

Natural Transformations: Adjunctions and Triangular Identities

Explores adjunctions, triangular identities, and natural transformations in category theory.

Adjunctions and Push Outs

Covers adjunctions, push outs, colimits, and discrete fibers in coverings, emphasizing group actions and symmetries.

Construction of Free Action Functor

Explores the construction of the free action functor in group theory and category theory, emphasizing group actions and their properties.

Generalization of Category Equivalence

Introduces an important generalization of category equivalence and its implications for group theory.

Natural Transformations: Definition

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

Natural Transformations in Group Theory

Introduces natural transformations in group theory and category theory, emphasizing their definition and significance.

Limits and colimits: Introduction, Chapter 1(c)

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

Limits and colimits as adjoints: Chapter 1(c)

Explores the characterization of limits and colimits as adjoints in category theory.