Metadata-Version: 2.1
Name: comch
Version: 0.1.0
Summary: A package to study commutativityup-to-coherent-homotopies
Home-page: UNKNOWN
Author: Anibal M. Medina-Mardones
Author-email: ammedmar@gmail.com
License: UNKNOWN
Description: [![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/ammedmar/comch/master?filepath=notebooks)
        
        # ComCH
        
        ComCH is a Python 3 package for the study of commutativity
        up-to-coherent-homotopies.
        
        ## Motivation
        
        Commutativity up-to-coherent-homotopies is a concept originated in
        algebraic topology. It has found modern uses in topological data
        analysis, motion planning, condensed matter physics and several other
        areas. An important challenge for the application of the mathematical
        ideas sourraounding this concept, which are often defined
        non-constructively, is to describe them in effective terms suitable for
        concrete computations. This package serves to bridge the gap between
        theoretical ideas and concrete applications, by implementing the
        structures needed to interact effectively with commutativity
        up-to-coherent-homotopies.
        
        ## Mathematical overview
        
        Following the pioneering work of Steenrod, Cartan, Adem, Stashef,
        Bordman-Vogt, May, Dyer-Lashof and others, today we understand the
        correct framework for the study of commutativity
        up-to-coherent-homotopies as the one provided by operads and PROPs. In
        particular, *E*<sub>*n*</sub>-operads play a central role parameterizing
        the different levels of homotopical commutativity. In this package, we
        focus on the category of chain complexes, and consider two models for
        the *E*<sub>∞</sub>-operad which are equipped with a filtrations by
        *E*<sub>*n*</sub>-operads. These models are respectively due to
        McClure-Smith [McS] and Berger-Fresse [BF] and are known as the
        surjection operad and Barratt-Eccles.
        
        ## Installation
        
        This package is written in Python 3 and has no dependencies. It can be
        installed from a terminal simply entering:
        
        `python3 -m pip install comch`
        
        ## References
        
        [McS]: J. McClure, and J. Smith. "Multivariable cochain operations and
        little n-cubes." Journal of the American Mathematical Society 16.3
        (2003): 681-704.
        
        [BF]: C. Berger, and B. Fresse. "Combinatorial operad actions on
        cochains." Mathematical Proceedings of the Cambridge Philosophical
        Society. Vol. 137. No. 1. Cambridge University Press, 2004.
Platform: UNKNOWN
Classifier: Programming Language :: Python :: 3
Classifier: License :: OSI Approved :: MIT License
Classifier: Operating System :: OS Independent
Requires-Python: >=3
Description-Content-Type: text/markdown
