symmetric monoidal (∞,1)-category of spectra
homotopy theory, (∞,1)-category theory, homotopy type theory
flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed…
models: topological, simplicial, localic, …
see also algebraic topology
Introductions
Definitions
Paths and cylinders
Homotopy groups
Basic facts
Theorems
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
monoid theory in algebra:
categorification
A monoidal category whose underlying category is a groupoid (hence all whose morphisms are invertible).
Equivalently: an -spatial groupoid whose unitors satisfy the triangle identities;
Equivalently: a 1-truncated -space/-space.
A monoidal groupoid is an -spatial groupoid such that the triangle identity is satisfied for all objects and :
The oidification of a monoidal groupoid is a (2,1)-category.
Last revised on May 17, 2022 at 10:50:26. See the history of this page for a list of all contributions to it.