Coherent homotopical algebras: Special gamma categories.

Title: Coherent homotopical algebras: Special gamma categories.
Identifier: AAI9405496
identifier: 9405496
Creator: Arroyo, Fangjun Hsu.
Contributor: Adviser: Alex Heller
Date: 1993
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: We introduce a theory of coherence for symmetric monoidal categories in the spirit of Segal and show that it is equivalent, in an appropriate sense, to MacLane's original notion. More precisely, we prove that "special {dollar}\Gamma{dollar} categories", the analogue of special {dollar}\Gamma{dollar} spaces, and coherently symmetric monoidal categories are one and the same. This is analogous to the situation in topology where special {dollar}\Gamma{dollar} spaces are precisely homotopical commutative monoids. In light of the observation that the category of small categories Cat bears a functorial Quillen model structure with respect the class of categorical equivalences: in fact, is a homotopy theory in the sense of Alex Heller, we may reinterpret the theorem as stating that coherently symmetric monoidal categories are precisely the homotopical commutative monoids within this new homotopy theory.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.