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Examples, Chapter 1(b): Adjunctions
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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.
Quasi-Categories: Active Learning Session
Covers fibrant objects, lift of horns, and the adjunction between quasi-categories and Kan complexes, as well as the generalization of categories and Kan complexes.
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Homotopy theory of chain complexes
Explores the homotopy theory of chain complexes, focusing on retractions and model category structures.
Homotopy Coherent Groups and Quasi-Categories
Covers the characterization of trivial Kan fibrations and the importance of homotopy coherent groups.
Adjunctions and Functor Categories: Exploring Connections
Covers adjunctions and functor categories, emphasizing their significance in category theory and applications in deep learning.
Relations in Computer Science
Explores the properties of relations in computer science, including equivalence relations and the partition of a set.
Functor Categories: (Co)Limits and Simplicial Sets
Explores (co)limits in functor categories and simplicial sets, including equalizers and coequalizers of simplicial maps.
Quillen pairs and Quillen equivalences: Derived functors
Explores Quillen pairs, equivalences, and derived functors in homotopical algebra.
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Covers the basics of sets and operations in mathematics, from set properties to advanced operations.