Concept

Functor represented by a scheme

Related lectures (32)

Introduces two fundamental examples of simplicial sets: the nerve of a small category and the singular simplicial set of a topological space.

Natural Transformations

Explores natural transformations between functors, emphasizing their composition-preserving properties and significance in category theory.

Derived functors: Identity and Homotopy Categories

Explores derived functors in model categories, focusing on identity and homotopy categories.

Homotopical Algebra

Covers the theory of groups and homotopical algebra, emphasizing natural transformations, identities, and isomorphism of categories.

Categories and Functors

Explores building categories from graphs and the encoding of information by functors.

Vertical Metronome: Equilibrium and Stability

Explores equilibrium and stability of a vertical metronome system with springs.

Categories and Functors: An Introduction

Provides an overview of categories, functors, and natural transformations in mathematics.

Natural Transformations in Algebra

Explores natural transformations in algebra, defining functors and isomorphisms.

Linear Algebra: Bases and Transformations

Covers bases, transformations, and matrix decompositions in linear algebra.

Untitled

Tangent Spaces and Submersions

Covers tangent spaces and submersions in differential geometry, emphasizing vector spaces and differentiable structures.

Free Action Functor: Left Adjoint to Forgetful Functor

Explores the free action functor as the left adjoint to the forgetful functor, emphasizing its equivalence-preserving properties and natural bijection.