Lectures related to Strict 2-category

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

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

Adjunctions and Limits: Exploring Functors and Co-limits

Covers adjunctions and limits, focusing on functors, co-limits, and their applications in category theory.

Natural Transformations in Algebra

Explores natural transformations in algebra, defining functors and isomorphisms.

Transfer of Model Structures

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

Category Theory: Introduction

Covers the basics of categories and functors, exploring properties, composition, and uniqueness in category theory.

Elementary Properties of Model Categories

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

Characterizing Fibrations in Chain Complexes

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

Quillen Equivalences

Explores Quillen equivalences, emphasizing the preservation of cofibrations and acyclic cofibrations.

Linear Applications and Simple Objects

Covers the bijection between linear applications from L(X) to V and applications from X to U(V).

Geometric Realization in Model Categories

Explores geometric realization, simplicial sets, and model category structures.

Lifting Properties in Model Categories: An Overview

Provides an overview of lifting properties in model categories, focusing on their definitions and implications for morphisms and commutative diagrams.

Quasicategories: An Alternative Homotopy Theory

Introduces quasicategories as an alternative approach to defining homotopy maps and categories.

Quillen pairs and Quillen equivalences: Derived functors

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

Categories and Functors

Covers categories, functors, and presheaf categories, exploring the relationships between objects and morphisms.

Lifting properties and model categories

Covers the study of lifting properties in categories, focusing on the left and right lifting properties.

Functors: Categories, Functors, and Natural Transformations

Introduces functors, including identity and forgetful functors, and explores duality functors.

Homotopy Categories: Model Structures

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

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.

Model Categories: Properties and Structures

Covers the properties and structures of model categories, focusing on factorizations, model structures, and homotopy of continuous maps.