On the surjectivity of the map of spectra associated to a tensor-triangulated functor.
2017
We prove a few results about the map $Spc(F)$ induced on tensor-triangular spectra by a tensor-triangulated functor $F$. First, $F$ is conservative if and only if $Spc(F)$ is surjective on closed points. Second, if $F$ detects tensor-nilpotence of morphisms then $Spc(F)$ is surjective on the whole spectrum. In fact, surjectivity of $Spc(F)$ is equivalent to $F$ detecting the nilpotence of some class of morphisms, namely those morphisms which are nilpotent on their cone.
Keywords:
- Correction
- Cite
- Save
- Machine Reading By IdeaReader
0
References
0
Citations
NaN
KQI