Strict 2-category

Formal sciences
Mathematics
Algebra
Abstract algebra

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (32)

Page 3 of 4

Introduction to Left Homotopy: The Homotopy Relation in a Model Category

Introduces left homotopy between morphisms and its preservation under postcomposition in a model category.

Basic properties of left homotopy: The homotopy relation in a model category

Explores the basic properties of left homotopy in model categories, focusing on weak equivalences and morphism relationships.

Limits and Colimits in Functor Categories

Explores limits and colimits in functor categories, focusing on equalizers, pullbacks, and their significance in category theory.

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.

Derived Functors in Homotopical Algebra

Covers the Fundamental Theorem of homotopical algebra, Quillen pairs, and derived functors.

Lifting properties, Chapter 2(a): Definition and elementary properties of model categories

Covers morphisms with lifting properties, pushouts, pullbacks, and the uniqueness in the universal property of pushouts.

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.

Model Category: Definition and Elementary Properties

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

The Whitehead Lemma: Homotopy Equivalence in Model Categories

Explores the Whitehead Lemma, showing when a morphism is a weak equivalence.

Introduction to Model Categories

Explores lifting properties and model categories in topological spaces.