Examples of Quasicategories

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Related lectures (41)

Homotopy Category of a Model Category

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

Homotopy Theory of Chain Complexes

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

Homotopy Theory: Cylinders and Path Objects

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

Elementary Properties of Model Categories

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

Homotopy theory of chain complexes

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

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.

Introduction to Model Categories

Explores lifting properties and model categories in topological spaces.

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.

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.

Quillen pairs and Quillen equivalences: Derived functors

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

Homotopical Algebra: The Homotopy Category of a Model Category

Focuses on proving the construction of the homotopy category and its properties, including preservation of composition and uniqueness of functors.

Model Category: Definition and Elementary Properties

Covers the definition and properties of a model category, including fibrations, cofibrations, weak equivalences, and more.

Derived functors: Two technical lemmas

Covers two technical lemmas essential for the Fundamental Theorem in homotopical algebra.

Topology: Homotopy and Projective Spaces

Discusses homotopy, projective spaces, and the universal property of quotient spaces in topology.

Sets of Left Homotopy Classes: The Homotopy Relation in a Model Category

Explores sets of left homotopy equivalence classes of morphisms in model categories.

Homotopy Theory of Chain Complexes

Explores the model structure on chain complexes over a field.

Homotopy: Fundamentals and Examples

Covers the fundamentals of homotopy and its applications in topology.

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.

Homotopical Algebra: Introduction Log in to Mediaspace to watch this video

Introduces the course on homotopical algebra, exploring the power of analogy in pure mathematics.

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