Presheaf (category theory)

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Related lectures (30)

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Adjunctions and Limits: Exploring Functors and Co-limits

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

Sheafification of Presheaves

Covers the sheafification process of presheaves, emphasizing injectivity and surjectivity.

Sheaves: Hartshorne I.1

Covers the concept of sheaves, emphasizing the unique determination of functions by local data and the importance of direct limits.

Infinity category theory: Equivalences and Adjunctions

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

Sheaves and Modules

Covers sheaves and modules, including morphisms, sheafification, cocalization, and direct image properties.

Sheafification: Natural Procedure and Adjoints

Covers sheafification, adjoint functors, and challenges in ensuring sheaf properties.

Review of Simplicial Sets

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

Homotopical Algebra: (Co)Limits

Explores the concept of (co)limits in homotopical algebra, discussing functor relations, special cases, and the universal properties of colimits and limits.

Introduction to Adjunctions in Category Theory

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

Limits and colimits as adjoints: Chapter 1(c)

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