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Concept

Presheaf (category theory)

Related lectures (30)

Introduces limits and colimits in a category, covering their properties and uniqueness.

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

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

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

Explores concrete examples of limits and colimits in functors and different categories.

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

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

Explores equivalences, adjunctions, and simplicial enrichment in infinity category theory.

Covers limits, colimits, standard simplices, mapping spaces, boundaries, horns, and spines.

Introduces adjunctions in category theory, exploring necessary conditions and natural transformations for adjoint functors.

Explores the characterization of limits and colimits as adjoints in category theory.

Explores how adjunctions relate to limits and colimits, proving their preservation properties.

Covers adjunctions, push outs, colimits, and discrete fibers in coverings, emphasizing group actions and symmetries.

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

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

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

Explores functors between categories and the conditions for left and right adjoints.

Explores equivariance in group actions and functors, demonstrating its importance in group theory.

Explores the concept of torsion in group theory, focusing on its Hom functoriality and its role in exact sequences.

Explores invariant definitions in sets, groups, and automorphisms, including p-divisible groups and free abelian groups.