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Construction junctions are diamonds. They show where multiple structures must coexist on the same carrier and satisfy compatibility conditions.

Canonical static concept record

Dagger category

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Summary

A category with an identity-on-objects involutive contravariant endofunctor.

Record metadata

Canonical name: Dagger category
Concept ID: dagger_category
Content version: 2.3.0
Primary field: Mathematics
Fields: Mathematics
Primary domain: Category theory
Domains: Category theory, Logic
Alternate terminology: No alternate terminology is currently authored for this record.

Carrier(s)

category $C$

Data

dagger $f\mapsto f^\dagger$

Axioms / constraints

$(f^\dagger)^\dagger=f$
$(g\circ f)^\dagger=f^\dagger\circ g^\dagger$

Concept sources

Wikipedia — Dagger category — Dagger category · expository · source ID wp-dagger-category
nLab — Dagger category — Dagger category · reference · source ID nlab-dagger-category
Riehl — Category Theory in Context — Category Theory in Context · textbook · source ID riehl-category-context

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

Category Dagger category

Permalink to relation

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

Relation ID: e_category_dagger
Relation type: Add data add-data
Direction: source → target
Endpoint roles: source: Builds toward; target: Built from
Authored annotation: + dagger involution

Authored explanation

Add an involutive identity-on-objects contravariant endofunctor.

How to interpret this relation type

Equip an existing carrier or structured object with additional chosen data, when such compatible data exists. Use a construction junction when several independently meaningful inputs must coexist on the same carrier or interact compatibly.

Relation sources

Wikipedia — Dagger category — Dagger category · expository · source ID wp-dagger-category
nLab — Dagger category — Dagger category · reference · source ID nlab-dagger-category
Riehl — Category Theory in Context — Category Theory in Context · textbook · source ID riehl-category-context

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.

No direct relations are authored in this direction.

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