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Concept

Pushout (category theory)

Related lectures (29)

Limits and Colimits in Functor Categories

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

Functor Categories: (Co)Limits and Simplicial Sets

Explores (co)limits in functor categories and simplicial sets, including equalizers and coequalizers of simplicial maps.

Limits and colimits: Two examples

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

Homotopy Identification

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

Introduction to Coproducts

Introduces coproducts in category theory, exploring their properties, universality, and relationships with products.

Limits and Colimits: Equalizers and Coequalizers

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

Direct Sums: Lemme 1.2

Delves into direct sums of abelian groups, showcasing their coproduct properties and universal verification.

Proof of Uniqueness

Explores the proof of uniqueness in coproducts through commutativity and universal properties.

Pushouts in Group Theory: Universal Properties Explained

Covers the construction and universal properties of pushouts in group theory.

Amalgams: Group Pushouts

Covers the concept of amalgams, defining pushouts and quotient groups in group theory.

Notation: Coproduct vs. Product

Explores the distinction between coproduct and product notation in categorical constructions within Abelian groups.

Fundamental Group of Wedge

Explores the fundamental group of a wedge and its applications.

Left Adjoint Preserves Coproducts

Explores how left adjoints preserve coproducts in category theory with detailed proofs and morphism diagrams.

Topology: Homotopy and Cone Attachments

Discusses homotopy and cone attachments in topology, emphasizing their significance in understanding connected components and fundamental groups.

Topology: Homotopy and Projective Spaces

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

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.

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.

Telescope Construction

Covers the construction of a telescope using cylinders on circles and the calculation of fundamental groups for various spaces.

Topology: Classification of Surfaces and Fundamental Groups

Discusses the classification of surfaces and their fundamental groups using the Seifert-van Kampen theorem and polygonal presentations.

Linear Applications and Simple Objects Log in to Mediaspace to watch this video

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