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dependent_product_functor [2015/12/22 18:01]
nikolaj
dependent_product_functor [2019/09/28 18:11] (current)
nikolaj
Line 96: Line 96:
 The point is that an arrow $\theta:​\pi_2\to p$ in ${\bf{C}}/​X$ exactly fulfills our condition by definition. A right adjoint $\prod_{!_X}$ to the pullback functor $!_X^*$ is defined as an isomorphism ​ The point is that an arrow $\theta:​\pi_2\to p$ in ${\bf{C}}/​X$ exactly fulfills our condition by definition. A right adjoint $\prod_{!_X}$ to the pullback functor $!_X^*$ is defined as an isomorphism ​
  
-$${\bf{C}}/​X[!_X{}^*!_A,​p]\cong{\bf{C}}/​X[!_A,​\prod_{!_X}p]$$+$${\bf{C}}/​X[!_X{}^*!_A,​p]\cong{\bf{C}}/​*[!_A,​\prod_{!_X}p]$$
  
 I.e. this provides an isomorphism of the above triangle to I.e. this provides an isomorphism of the above triangle to
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