Lectures related to Pullback (category theory)

Limits and colimits: Two examples

Focuses on the pushout and pullback constructions in sets, illustrating colimits and limits with explicit examples.

Introduction to Category Theory: Examples

Introduces the theory of categories through examples and discusses the product of categories.

Homotopy Identification

Delves into homotopy identification, pushout diagrams, colimits, and group fundamental calculations.

Quotients de groupe: Un cas particulier

Explores a categorical perspective on group quotients, focusing on a specific case.

Construction of Free Action Functor

Explores the construction of the free action functor and its equivariance.

Cofibrations: Extension Property and Recognition Principle

Explores the extension property of spaces and the recognition principle for cofibrations.

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.

Electromagnetic Problems: Well-Posedness and Convergence

Explores the well-posedness and convergence of electromagnetic problems, including continuity interpolation, Darcy's law, and surjectivity properties.

Limits and Colimits in Functor Categories

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

Triangular Identities

Covers triangular identities, natural transformations, commutative diagrams, and adjunction notation in group and category theory.

Modular Forms: Dimension Formula

Explores modular forms, discussing pullback maps, meromorphic differentials, and the Riemann-Roch theorem.

Cohomology Real Projective Space

Covers cohomology in real projective spaces, focusing on associative properties and algebraic structures.

The Five Lemma

Covers the Five Lemma, a fundamental result in exact sequences theory.

The Lemma of the Five: Abelian Groups

Presents the Lemma of the Five, a fundamental result in group theory.

Limits and Colimits: Equalizers and Coequalizers

Covers limits and colimits, focusing on equalizers and coequalizers in category theory.

Topology: Lecture Notes 2021

Covers commutative diagrams, homotopy, and constructing topological spaces.

Adjunctions and Limits: Exploring Functors and Co-limits

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

Introduction to Model Categories

Explores lifting properties and model categories in topological spaces.

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.