+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ### Context #### Homotopy theory +-- {: .hide} [[!include homotopy - contents]] =-- #### Type theory +-- {: .hide} [[!include type theory - contents]] =-- =-- =-- #Contents# * table of contents {:toc} ## Idea In [[homotopy theory]] and [[homotopy type theory]], by *truncation* one means the [[reflective subcategory|reflection]] onto [[truncated objects]]. ## Related entries * For discussion in [[homotopy type theory]] (mostly) see: * [[h-level]] * [[contractible type]], [[mere proposition]], [[h-set]], [[h-groupoid]] * [[cone type]] or (-2)-truncation * [[propositional truncation]] or (-1)-truncation * [[set truncation]] or 0-truncation * [[n-truncation modality]] * For discussion in [[higher category theory]], see: * [[truncated object]] * [[homotopy n-type]] * [[Postnikov tower]] * [[truncation of a chain complex]] * [[n-truncated object of an (infinity,1)-category]] * [[(n+1,1)-category of n-truncated objects]] * [[(n-connected, n-truncated) factorization system]] [[!redirects truncated]] [[!redirects truncation]] [[!redirects truncations]] [[!redirects (-2)-truncated]] [[!redirects (-2)-truncation]] [[!redirects (-2)-truncations]] [[!redirects (-1)-truncated]] [[!redirects (-1)-truncation]] [[!redirects (-1)-truncations]] [[!redirects 0-truncated]] [[!redirects 0-truncation]] [[!redirects 0-truncations]] [[!redirects 1-truncated]] [[!redirects 1-truncation]] [[!redirects 1-truncations]] [[!redirects 2-truncated]] [[!redirects 2-truncation]] [[!redirects 2-truncations]] [[!redirects 3-truncated]] [[!redirects 3-truncation]] [[!redirects 3-truncations]] [[!redirects 4-truncated]] [[!redirects 4-truncation]] [[!redirects 4-truncations]] [[!redirects n-truncated]] [[!redirects n-truncation]] [[!redirects n-truncations]] [[!redirects k-truncated]] [[!redirects k-truncation]] [[!redirects k-truncations]]