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Thin category

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Summary

A category with at most one morphism between any ordered pair of objects.

Record metadata

Carrier(s)

Data

Axioms / constraints

Canonically induces

Concept sources

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

CategoryThin category

Permalink to relation

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

Authored explanation

Require each hom-set to have at most one element.

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

PreorderThin category

Permalink to relation

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

Authored explanation

Use elements as objects and a unique morphism xyx\to y exactly when xyx\le y; thin categories conversely determine preorders on their objects.

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

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.

No direct relations are authored in this direction.