The following is my research on sheaves and human memory. It is based on essay by Lovering. I have been extracting important points and generalizing his ideas. https://tlovering.files.wordpress.com/2011/04/sheaftheory.pdf

Here is a snippet of my introduction.

Memory is Processing of Data

-memory what happens as a result of processing information

Depth of Processing of Information

Shallow Processing

-sensory memory: appearance, physical qualities, sound

Deep Processing

-encode meaning, relating similar environments and circumstances

-deeper level of processing, easier information recalled

source: Memory, Encoding Storage and Retrieval | Simply Psychology

Sheaf Theory - Lovering

General Learning Process

-certain field of interest

-collection of facts, ideas, examples

-maybe necessary to restrict area of study, specialized area

-sometimes apply interesting way, sometimes trivial

-similar ideas in different area of interest

-maybe two ideas contrast: deduce relationship

-arise general theory that envelops ideas

-glue different areas together depending on similarity

Sheaf Action A: Limited Data

-let topological space and attaching data to it

-restriction: only capable of perceiving some of the topology such that some of the data be hidden

-brain reconstructs data based on topology (incomplete information)

-end result: abstraction of data and reassembly of data

-unique, nicely-behaved sheaf arises from open data sets on a topology (after restriction) when gluing exists

-sheaves have structure: depending on restriction maps

Sheaf Action B: Local Properties

-whether that data on topological space is compatible (or gluable)

-study of smooth functions on manifold

-functions may not be explicitly defined

-we work with local properties

-sensory memory, preconceptions, judging factuality

Section Results

Data management: Sections, Data Restriction

Define a Presheaf pp2

Let presheaf F of a category

Topological space X

1) Every open set U subset X a group F(U),

2) Every inclusion U subset V a group homomorphism rho_{VU}: F(V) to F(U)

1)-F(U) is called Section

2)-Restriction map is a Morphism

A sheaf is a mathematical concept that holds local information on open sets. A google search will reveal that sheaf (math) ideas apply to memory models through computation. Please help generalize mathematical theorems starting from page 3 of Lovering. Work needs to be done regarding manifolds, schemes, and sheaf cohomology: modules and complexes.

This is not a school project. It is my hobby that can become something more. Any work will be accredited to your name. Making this a featured discussion would be great!

Thanks all for your time.

Arthur