Equivalence of coherent theories

✍ Scribed by Nikita Shekutkovski

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 594 KB
• Volume: 75
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(96)00094-6

✦ Synopsis

In a series of papers Yu. Lisica and S. MardeSiC developed a coherent theory of inverse systems X = (X,,P,,,,, > A). where for a11 < al < UZ, paga,pala2 = P,"~*, and the corresponding strong shape theory. A coherent map between two systems f: X + Yis defined by homotopies of all orders. Category CPHTop has as objects inverse systems X and as morphisms homotopy classes of coherent maps.

A more general type of inverse systems are the systems X = (Xarp," ..a,, A) where the equation above is replaced by existence of a homotopy pa,,a,a, : 1 x X,, + X,, connecting maps paga,pala2 and paoa2, but also in this system there exist homotopies pa,,...a, : I"-' x X,, + X,, of arbitrary order which on the boundary al"-' x X,, are defined by homotopies of lower order. The coherent category of these systems is denoted by Coh.

Inverse systems X can be considered as objects of Coh and actually CPHTop is a subcategory of Coh. In this paper we positively solve the problem: Is CPHTop a full subcaregorq of Coh?