User:Leigh.Samphier/Topology/Definition:Category of Locales with Localic Mappings
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Definition
The category of locales with localic mappings, denoted $\mathbf{Loc_*}$, is the category with:
Objects: | locales, that is, Complete Lattices $\struct{L, \preceq}$ satisfying infinite join distributive law | |
Morphisms: | Localic Mappings, that is, mappings that are the upper adjoint to a frame homomorphism | |
Composition: | Standard composition of mappings | |
Identity morphisms: | $\operatorname{id}_{\struct {L, \preceq} } := \operatorname{id}_L$, the identity mapping on $L$ |
Also see
Sources
- 2012: Jorge Picado and Aleš Pultr: Frames and Locales: Chapter II: Frames and Locales. Spectra, $\S 2.2$