topos theory

# Contents

## Definition

A locally ringed space is a ringed space $(X,\mathcal{O})$ such that the stalks of the structure sheaf $\mathcal{O}$ are local rings.

A morphism of locally ringed space is a morphism of ringed spaces $(f,f^\sharp):(X,\mathcal{O}_X)\to (Y,\mathcal{O}_Y)$, where $f:X\to Y$, such that the comorphism $f^\sharp:\mathcal{O}_Y\to f_*\mathcal{O}_X$ is a morphism of local rings (that is, a map of rings which respects the maximal ideal).

## References

Revised on November 22, 2013 03:30:49 by Urs Schreiber (77.251.114.72)