Simplicial sets

a geometrical object (set composed of points, line segments, triangles, and their n-dimensional counterpart) useful to describe certain topological spaces

small category, whose objects are sets of natural numbers of the form {0,1,…,n}, and whose morphisms are nondecreasing functions

construction in categorical homotopy theory; contravariant functor from the simplex category to the category of sets

simplicial complex associated to an open cover of a topological space

formalism for producing simplicial approximations of spacetimes

study of discrete counterparts of notions in differential geometry

in algebraic topology, a theorem that a continuous map between (geometric realizations of) simplicial complexes is homotopy-equivalent to a simplicial map between subdivisions of the simplicial complexes