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Lecture
Homotopy Theory in Chain Complexes
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Understanding Lifting Properties in Homotopy Theory
Focuses on lifting properties in homotopy theory of chain complexes.
Homotopy theory of chain complexes
Explores the homotopy theory of chain complexes, focusing on defining cylinder objects and left homotopy.
Cohomology: Cross Product
Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.
Model Categories: Properties and Structures
Covers the properties and structures of model categories, focusing on factorizations, model structures, and homotopy of continuous maps.
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.
Homotopy Theory of Chain Complexes
Explores the model structure on chain complexes over a field.
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.
Homotopy Coherent Groups and Quasi-Categories
Covers the characterization of trivial Kan fibrations and the importance of homotopy coherent groups.
Homotopy Theory of Chain Complexes
Explores the homotopy theory of chain complexes over a field, focusing on closure properties and decomposition.
Acyclic Models: Cup Product and Cohomology
Covers the cup product on cohomology, acyclic models, and the universal coefficient theorem.
