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Lecture
Infinity Category Theory: Lecture 2
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Model Categories and Homotopy Theory: Functorial Connections
Covers the relationship between model categories and homotopy categories through functors preserving structural properties.
Serre model structure: Left and right homotopy
Explores the Serre model structure, focusing on left and right homotopy equivalences.
Derived functors: Identity and Homotopy Categories
Explores derived functors in model categories, focusing on identity and homotopy categories.
Homotopy Theory of Chain Complexes
Explores the homotopy theory of chain complexes, focusing on model categories, weak equivalences, and the retraction axiom.
Quillen pairs and Quillen equivalences: Derived functors
Explores Quillen pairs, equivalences, and derived functors in homotopical algebra.
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.
Serre model structure on Top
Explores the Serre model structure on Top, focusing on right and left homotopy.
The Whitehead Lemma: Homotopy Equivalence in Model Categories
Explores the Whitehead Lemma, showing when a morphism is a weak equivalence.
Homotopy Theory in Care Complexes
Explores the construction of cylinder objects in chain complexes over a field, focusing on left homotopy and interval chain complexes.
Quillen Equivalences
Explores Quillen equivalences, emphasizing the preservation of cofibrations and acyclic cofibrations.
