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Transformations between acsets involving only combinatorial data #806

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merged 2 commits into from Oct 3, 2023

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@kris-brown kris-brown commented Jun 14, 2023

By considering CSetTransformations between ACSets (where naturality is not demanded on attributes) we can obtain two sorts of practical constructions:

  1. A kind of "labeled CSet" where we can think of the attributes as functioning as labels
  2. A kind of limit construction for ACSets which acts purely on the combinatorial data. The apex can put whatever it wants for the attributes, but we can deliberately pick a representative of the isomorphism class to make it correspond to something meaningful (with valid ACSetTransformations), which Kevin has a nice categorical characterization of in an AlgebraicJulia blog post.

Implementation-wise, this means we want an abstract type of ACSetMorphism which is implemented by ACSetTransformation and CSetTransformation (therefore, this is changing the meaning of CSetTransformation, which before was an ACSetTransformation that happened to be on a schema with no attributes). There is probably a lot of functionality which is written for ACSetTransformation which would straightforwardly work for ACSetMorphism, but the minimal required functionality (e.g. dom, compose) for getting limits to work is all that is generalized for now.

It may be the case that we want something in between, where a subset of the attributes are marked to be ignored. This would give us a kind of "LACSets" - but we would then lose the ability to do #2 above, which I see as the real value of this.

Edit: I also addressed a tiny bug in the HomSearch code where monic and iso fast failure constraints were not being checked for the combinatorial Attr data.

@kris-brown kris-brown changed the title Pragmatic product of varacsets and a generalized stratification Abstracted product of varacsets and a generalized stratification Jun 21, 2023
@epatters epatters force-pushed the stratification branch 2 times, most recently from 8dbb553 to 4356d1d Compare July 20, 2023 16:40
@kris-brown kris-brown changed the title Abstracted product of varacsets and a generalized stratification Abstracted product of varacsets Jul 21, 2023
@kris-brown kris-brown changed the title Abstracted product of varacsets Category of ACSets and CSetTransformations Aug 24, 2023
@kris-brown kris-brown self-assigned this Aug 24, 2023
@AlgebraicJulia AlgebraicJulia deleted a comment from github-actions bot Oct 2, 2023
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Very nice! I just left a few small comments.

src/categorical_algebra/CSets.jl Show resolved Hide resolved
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@epatters epatters changed the title Category of ACSets and CSetTransformations Transformations between acsets involving only combinatorial data Oct 2, 2023
Kris Brown added 2 commits October 3, 2023 13:56
loose kwarg for product and terminal

example where distinguished object is not a leaf object

SigmaMigration can return a DiagramHom with components kwarg

master -> main

Pragmatic -> abstract

no stratify nor box product for now

CSetTransformations

cleanup

cascade effect of fixing homsearch bug

finish rebase
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Thanks Kris!

@epatters epatters merged commit 1874704 into AlgebraicJulia:main Oct 3, 2023
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@kris-brown kris-brown deleted the stratification branch October 3, 2023 23:44
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