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Derived Direct and Inverse Image

A basic objective, in the spirit of Grothendieck s philosophy of the six operations, is the categorical formalization of relations among functorial maps involving the four operations R/, L/, and RWom.  [Pg.83]

More explicitly (details in 3.4, 3.5), if / X F is a map of ringed spaces, then the derived categories D( x), D( Ay) have natural structures of symmetric monoidal closed categories, given by g) and RTfom and the adjoint A-functors R/ and L/ respect these structures, as do the conjugate isomorphisms, arising from a second map g Y Z, R gf)t R R/, Lf Lg L gf). We express all this by saying that R— and L— are adjoint monoidal A-pseudofunctors. [Pg.83]

relations among the four operations can be worked with as instances of category-theoretic relations involving adjoint monoidal functors between [Pg.83]

The second and third maps determine each other via L/ -R/ adjunction (3.4.5), as do the third and fourth (3.4.6). When the first map is given, the second and third maps also determine each other via RWom - adjunction. (This is not obvious, see Proposition (3.2.4).) [Pg.84]

any three of the four maps can be deduced category-theoretically from the remaining one. [Pg.84]


Adjointness of Derived Direct and Inverse Image corresponds via (2.6.1) to the composed map... [Pg.95]

We review next the behavior of derived direct and inverse image functors vis-a-vis a pair of ringed-space maps X Y Z. [Pg.118]

Derived Direct and Inverse Image For commutativity, expand the diagram naturally as follows. [Pg.150]


See other pages where Derived Direct and Inverse Image is mentioned: [Pg.83]    [Pg.84]    [Pg.86]    [Pg.88]    [Pg.89]    [Pg.89]    [Pg.89]    [Pg.90]    [Pg.91]    [Pg.92]    [Pg.93]    [Pg.94]    [Pg.96]    [Pg.98]    [Pg.100]    [Pg.102]    [Pg.104]    [Pg.106]    [Pg.108]    [Pg.110]    [Pg.112]    [Pg.114]    [Pg.116]    [Pg.118]    [Pg.120]    [Pg.122]    [Pg.124]    [Pg.126]    [Pg.128]    [Pg.130]    [Pg.132]    [Pg.132]    [Pg.134]    [Pg.136]    [Pg.138]    [Pg.140]    [Pg.142]    [Pg.144]    [Pg.146]    [Pg.148]    [Pg.152]    [Pg.154]    [Pg.156]    [Pg.158]   


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Adjointness of Derived Direct and Inverse Image

And inversion

Direct image

Direct imaging

Directional derivative

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