Lectures related to Kan fibration

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.

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.

Functors and Adjunctions

Explores functors between categories and the conditions for left and right adjoints.

Schematic Models: Quasi-Categories and ∞-Groupoids

Covers schematic models, emphasizing quasi-categories and ∞-groupoids in modeling categories.

Serre model structure on Top

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

The Nerve and Geometric Realization

Delves into the computation and geometric realization of small categories, exploring the relationship between nerves and geometric structures.

Homotopy Category of a Model Category

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

Homotopy Categories: Model Structures

Explores homotopy categories in model structures, emphasizing weak equivalences and the Whitehead Lemma.

Nerves and Geometric Realization

Covers the explicit computations of nerves of categories and geometric realisations of simplicial sets.

Characterizing Fibrations in Chain Complexes

Explores the characterization of fibrations and acyclic fibrations in chain complexes.

The Joyal Model Structure

Defines and studies the Joyal Model structure, focusing on the properties of quasi-categories within this framework.

CW Pairs: Homotopy Extension Property

Discusses how CW pairs satisfy the homotopy extension property through retractions and homotopy extension properties.

Homotopy Theory: Cylinders and Path Objects

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

Homotopy Extension Property

Demonstrates how to obtain homotopy equivalences between different spaces using the homotopy extension property.

Homotopy Theory of Chain Complexes

Explores the homotopy theory of chain complexes, including path object construction and fibrations.

Homotopy theory of chain complexes

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

Homotopy theory of chain complexes

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

Natural Examples of Simplicial Sets

Introduces two fundamental examples of simplicial sets: the nerve of a small category and the singular simplicial set of a topological space.

Infinity Category Theory: Extensions and Equivalences

Explores right extensions in infinity category theory and their equivalent definitions.