natural deduction metalanguage, practical foundations
type theory (dependent, intensional, observational type theory, homotopy type theory)
computational trinitarianism =
propositions as types +programs as proofs +relation type theory/category theory
Basic structures
Generating functions
Proof techniques
Combinatorial identities
Polytopes
In dependent type theory (homotopy type theory), by -finite types one means a kind of finite types which are not necessarily h-sets but have finite homotopy groups in each degree (what in homotopy theory are called a pi-finite homotopy types or similar).
For given natural number , a type is called -finite if
it has a finite type of connected components (0-truncation),
all its homotopy groups up to h-level at all base points are finite.
A type is -finite type if it is -finite for all .
Given two -finite types and , the types and are both -finite types. Similarly, given a family of -finite types indexed by a -finite type , the dependent sum type is a -finite type.
Given a univalent universe and a natural number ,
the type of all -small types with elements is a -finite type.
The type of all -small finite groups of order is a -finite type.
UniMath project, π-finite types (web)
UniMath project, Univalent combinatorics (web)
Last revised on August 12, 2023 at 13:30:47. See the history of this page for a list of all contributions to it.