Accession Number : AD0480191

Title :   4348-M POLYGROUPOIDS.

Descriptive Note : Rept. no. 2 (Final) 17 Jul 64-30 Sep 65,

Corporate Author : OHIO STATE UNIV RESEARCH FOUNDATION COLUMBUS

Personal Author(s) : Zilber, Joseph A.

Report Date : 14 MAR 1966

Pagination or Media Count : 7

Abstract : A polygroupoid is, essentially, a cubical complex whose set of n-cells constitutes a semigroupoid in n different ways (directions), with appropriate consistency properties. Notions of equivalence of polygroupoids and of quotient polygroupoids are defined; various polygroupoids are associated functorially with arbitrary semigroupoids and with topological spaces. The main theorem asserts the equivalence between the polygroupoid associated with a cellular complex (the latter being regarded as a semigroupoid) and that associated with the topological space which is the geometric realization of the complex.

Descriptors :   (*ALGEBRAIC TOPOLOGY, THEOREMS), GROUPS(MATHEMATICS), SEQUENCES(MATHEMATICS).

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE