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Lecture
Quasicategories: An Alternative Homotopy Theory
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Model Categories: Properties and Structures
Covers the properties and structures of model categories, focusing on factorizations, model structures, and homotopy of continuous maps.
Transfer of Model Structures
Covers the transfer of model structures through adjunctions in the context of model categories.
Adjunction between Simplicial Sets and Enriched Categories
Covers the adjunction between simplicial sets and simplicially enriched categories, including preservation of inclusions and construction of homotopy categories.
Natural Transformations in Algebra
Explores natural transformations in algebra, defining functors and isomorphisms.
Introduction to Model Categories
Explores lifting properties and model categories in topological spaces.
Lifting properties, Chapter 2(a): Definition and elementary properties of model categories
Covers morphisms with lifting properties, pushouts, pullbacks, and the uniqueness in the universal property of pushouts.
Category Theory: Introduction
Covers the basics of categories and functors, exploring properties, composition, and uniqueness in category theory.
Elementary Properties of Model Categories
Covers the elementary properties of model categories, emphasizing the duality between fibrations and cofibrations.
The Whitehead Lemma: Homotopy Equivalence in Model Categories
Explores the Whitehead Lemma, showing when a morphism is a weak equivalence.
Active Learning: Functors and Geometric Realization
Covers the computation of nerves and geometric realization in simplicial sets, along with functors into and out of the category of simplicial sets.
