Category theory

Related lectures (32)

Categories and Functors

Explores building categories from graphs and the encoding of information by functors.

Categories and Functors

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

Homotopy theory of chain complexes

Explores the homotopy theory of chain complexes, focusing on retractions and model category structures.

Categories: Functors, and Natural Transformations

Introduces categories, concrete examples, opposite categories, and isomorphisms, leading to groupoids.

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.

Limits and Colimits in Functor Categories

Explores limits and colimits in functor categories, focusing on equalizers, pullbacks, and their significance in category theory.

Adjunctions and Limits: Exploring Functors and Co-limits

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

Adjunctions: Constructing Desired Adjoints

Explores constructing desired adjoints in specific categories like Set.

Adjunctions and Functor Categories: Exploring Connections

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

Simplicial and Cosimplicial Objects: Examples and Applications

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

Categories and Functors: An Introduction

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

Transfer of Model Structures

Covers the transfer of model structures through adjunctions in the context of model categories.

Group Actions: G-objects in a Concrete Category

Explores G-objects in a concrete category and the framework for group actions.

Review of Simplicial Sets

Covers limits, colimits, standard simplices, mapping spaces, boundaries, horns, and spines.

Functors and Adjunctions

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

Functors: Categories, Functors, and Natural Transformations

Introduces functors, including identity and forgetful functors, and explores duality functors.

Functor Categories: (Co)Limits and Simplicial Sets

Explores (co)limits in functor categories and simplicial sets, including equalizers and coequalizers of simplicial maps.

Functor Categories Composition and Induced Functors

Explores composition of functors, induced functors, and preservation of commutative diagrams in category theory.

Natural Transformations Composition

Covers the theory of categories, emphasizing the importance of naturalness in the composition of transformations.

Limits and colimits: Introduction, Chapter 1(c)

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