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  1. No Access

    Chapter

    DERIVED FUNCTORS

    Let A be an abelian category. We will define the category Co(A) of (cochain) complexes as follows. An object in Co(A) is a sequence of objects and morphisms

    Goro Kato in The Heart of Cohomology (2006)

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    Chapter

    DERIVED CATEGORIES

    Let A be an abelian category and let Co+(A) be the category of bounded from below complexes as before.

    Goro Kato in The Heart of Cohomology (2006)

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    Chapter

    CATEGORY

    The notion of a category is a concise concept shared among “groups and group homomorphisms”, “set and set-theoretic map**s”, “topological spaces and continuous map**s”, e t c.

    Goro Kato in The Heart of Cohomology (2006)

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    Chapter

    SPECTRAL SEQUENCES

    A spectral sequence in an abelian category A consists of doubly indexed objects of A:

    Goro Kato in The Heart of Cohomology (2006)

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    Chapter

    COHOMOLOGICAL ASPECTS OF ALGEBRAIC GEOMETRY AND ALGEBRAIC ANALYSIS

    The most fundamental object of study in Algebraic Geometry is the set of (or the number) of solutions of a system of (polynomial) equations.

    Goro Kato in The Heart of Cohomology (2006)