Definition:Category of Frames
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Definition
The category of frames, denoted $\mathbf{Frm}$, is the category with:
| Objects: | Frames, that is, Complete Lattices $\struct{L, \preceq}$ satisfying infinite join distributive law | |
| Morphisms: | Frame Homomorphisms, that is, mappings that are both finite meet preserving and arbitrary join preserving | |
| Composition: | Standard composition of mappings | |
| Identity morphisms: | $\operatorname{id}_{\struct {L, \preceq} } := \operatorname{id}_L$, the identity mapping on $L$ |
Also see
Sources
- 1982: Peter T. Johnstone: Stone Spaces: Chapter $\text {II}$: Introduction to Locales, $\S 1.1$ Definition (a)