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Homotopical Algebra Exam
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Related lectures (23)
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Homotopical Algebra
Covers the theory of groups and homotopical algebra, emphasizing natural transformations, identities, and isomorphism of categories.
Homotopical Algebra: Examples and Adjunctions
Explores homotopical algebra examples and adjunctions, focusing on left and right adjoints in group functors and coproducts.
Homotopical Algebra: Theory and Applications
Explores homotopical algebra, covering colimits, limits, adjunctions, and their applications in group theory.
Homotopical Algebra: (Co)Limits
Explores the concept of (co)limits in homotopical algebra, discussing functor relations, special cases, and the universal properties of colimits and limits.
Derived functors: Two technical lemmas
Covers two technical lemmas essential for the Fundamental Theorem in homotopical algebra.
Left Homotopy as an Equivalence Relation: The Homotopy Relation in a Model Category
Explores the left homotopy relation as an equivalence relation in model categories.
Elementary Properties of Model Categories
Covers the elementary properties of model categories, emphasizing the duality between fibrations and cofibrations.
Existence of Left Derived Functors: Part 2
Concludes the proof of the existence of left derived functors and discusses total left and right derived functors.
The Whitehead Lemma: Homotopy Equivalence in Model Categories
Explores the Whitehead Lemma, showing when a morphism is a weak equivalence.
Homotopical Algebra: Functor and Adjunctions
Delves into homotopical algebra, defining functors and adjunctions with examples.
