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Frame / complete Heyting algebra

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Summary

A complete lattice in which finite meets distribute over arbitrary joins.

Record metadata

Carrier(s)

Axioms / constraints

Canonically induces

Concept sources

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

Complete latticeFrame / complete Heyting algebra

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

Require finite meets to distribute over arbitrary joins.

How to interpret this relation type

Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.

Relation sources

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.

Frame / complete Heyting algebraHeyting algebra

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

A frame canonically has Heyting implication given by the right adjoint to finite meet.

How to interpret this relation type

Pass canonically from a stronger object to structure it determines, or forget part of the data while retaining a valid weaker structure. The carrier may change under a canonical induced construction.

Relation sources

Frame / complete Heyting algebraLocale

Permalink to relation

This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

Regard the frame as the lattice of opens of a point-free space.

How to interpret this relation type

Reinterpret an object, pass to an equivalent presentation, or relate canonically corresponding structures; the carrier may change.

Relation sources