Functor Categories: (Co)Limits and Simplicial Sets

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Categories and Functors

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

Introduction to simplicial sets: Simplicial sets

Introduces the category of simplicial sets and explores the standard n-simplex as a universal example.

Functors and Adjunctions

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

Limits and colimits as adjoints: Chapter 1(c)

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

Categories and Functors

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

Limits and colimits: Concrete Examples

Explores concrete examples of limits and colimits in functors and different categories.

The Simplex Category: Simplicial Sets

Covers the combinatorics of the simplex category and its equivalence to topological spaces, as well as the concept of functor categories for cosimplicial and simplicial objects.

Limits and Colimits: Equalizers and Coequalizers

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

Adjunctions and Functor Categories: Exploring Connections

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

Limits and colimits: Introduction, Chapter 1(c)

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