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dependent_product_functor [2015/12/22 18:01] nikolaj |
dependent_product_functor [2019/09/28 18:11] (current) nikolaj |
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| 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 | ||
