Quasi-Categories: Active Learning Session

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Related lectures (33)

Homotopy Coherent Groups and Quasi-Categories

Covers the characterization of trivial Kan fibrations and the importance of homotopy coherent groups.

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.

Homotopy Theory of Chain Complexes

Explores the homotopy theory of chain complexes, focusing on model categories, weak equivalences, and the retraction axiom.

Serre model structure on Top

Explores the Serre model structure on Top, focusing on right and left homotopy.

Simplicial and Cosimplicial Objects: Examples and Applications

Covers simplicial and cosimplicial objects in category theory with practical examples.

Homotopy theory of chain complexes

Explores the homotopy theory of chain complexes, focusing on retractions and model category structures.

Quillen pairs and Quillen equivalences: Derived functors

Explores Quillen pairs, equivalences, and derived functors in homotopical algebra.

Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Homotopy Theory of Chain Complexes

Explores the model structure on chain complexes over a field.

Serre model structure: Left and right homotopy

Explores the Serre model structure, focusing on left and right homotopy equivalences.

Elementary Properties of Model Categories

Covers the elementary properties of model categories, emphasizing the duality between fibrations and cofibrations.

Homotopy Theory: Cylinders and Path Objects

Covers cylinders, path objects, and homotopy in model categories.

Homotopy theory of chain complexes

Explores the homotopy theory of chain complexes, focusing on defining cylinder objects and left homotopy.

Homotopy Theory in Chain Complexes

Explores acyclic fibrations and cylinder objects in chain complexes.

The Topological Künneth Theorem

Explores the topological Künneth Theorem, emphasizing commutativity and homotopy equivalence in chain complexes.

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 Category and Derived Functors

Explores the homotopy category of chain complexes and the relation between quasi-isomorphisms and chain homotopy equivalences.

Homotopy Category of a Model Category

Introduces the homotopy category of a model category with inverted weak equivalences and unique homotopy equivalences.

Infinity Category Theory: Lecture 2

Explores infinity category theory, covering ABB, Kao-cosmos, homotopy, categories, and equivalences.

Transfer of Model Structures

Covers the transfer of model structures through adjunctions in the context of model categories.

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