Keyboard graph navigation: press N for concepts or E for relations; use arrow keys, Home, and End to move; Enter selects; Shift plus Enter selects and centers; plus and minus zoom; zero fits; Escape clears the selection. Use the visible viewport buttons as alternatives to dragging, wheel, and pinch gestures.
Canonical static concept record
Open this concept in the interactive graphRead the Markdown equivalent
A collection of objects and morphisms with identities and associative composition; size is controlled by an ambient set-theoretic convention.
“Category” does not by itself mean small. A separate Small category node records the set-sized case.
wp-categorynlab-categorystacks-categoriesriehl-category-contextEach relation below ends at this concept.
No direct relations are authored in this direction.
Each relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Choose a terminal object and binary products satisfying their universal properties.
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.
wp-cartesian-categoryriehl-category-contextThis is an authored directed relation from the source endpoint to the target endpoint.
Add an involutive identity-on-objects contravariant endofunctor.
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.
wp-dagger-categorynlab-dagger-categoryriehl-category-contextThis is an authored directed relation from the source endpoint to the target endpoint.
Require every finite diagram to have a limit.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
nlab-finite-limitsriehl-category-contextThis is an authored directed relation from the source endpoint to the target endpoint.
Choose a target category and specify object and morphism assignments that preserve identities and composition.
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.
riehl-category-contextThis is an authored directed relation from the source endpoint to the target endpoint.
Require every morphism to have a two-sided inverse.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-groupoidriehl-category-contextThis is an authored directed relation from the source endpoint to the target endpoint.
Supply the category in which the diagram takes values.
Feed several structures into a construction junction and impose compatibility between them.
stacks-simplicial-objectsnlab-simplicial-objectwp-cosimplicial-objectriehl-category-contextThis is an authored directed relation from the source endpoint to the target endpoint.
Supply the category in which the diagram takes values.
Feed several structures into a construction junction and impose compatibility between them.
stacks-simplicial-objectsnlab-simplicial-objectriehl-category-contextThis is an authored directed relation from the source endpoint to the target endpoint.
Add three morphism classes satisfying Quillen model-category axioms.
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.
wp-model-categorynlab-model-categorystacks-derived-texthovey-model-categoriesThis is an authored directed relation from the source endpoint to the target endpoint.
Add a tensor bifunctor, unit object, associator, and unitors satisfying coherence.
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.
nlab-monoidal-categoryriehl-category-contextThis is an authored directed relation from the source endpoint to the target endpoint.
Give each hom-set an abelian-group structure and make composition bilinear.
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.
wp-preadditive-categoryriehl-category-contextThis is an authored directed relation from the source endpoint to the target endpoint.
Require the collections of objects and morphisms to be sets.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-categorynlab-categorystacks-categoriesriehl-category-contextThis is an authored directed relation from the source endpoint to the target endpoint.
Require each hom-set to have at most one element.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-thin-categoryriehl-category-context