(co)products/(co)equalizers for Fincats and Diagrams #609

kris-brown · 2022-03-18T19:55:35Z

Main goal: implement the constructions described in Peschke and Tholen (2020) remark 2.8. This involves developing a lot of other prerequisite functionality.

Main contributions:

Currying FinDomFunctors into C-Set as FinDomFunctors into Set
pushout-based chase
- Collage of functor
- Conversion between C-Set and SpanC-Set (a model for C-Rel)
- left kan extensions of FinDomFunctors into Set (or C-Set) + universal property
Limits/colimits the category of FinCats
- Products and coproducts of FinCat presentations (including treatment of equations)
- No treatment of equations yet for equalizers/coequalizers
Limits/colimits the category of FinCats
- Products/coproducts of Diagram{id} and Diagram{op}, equalizers for the former and coequalizers for the latter
- Universal properties for the above (co)limits
- Left kan extension used to compute coequalizers for Diagram{id}

To-do:

Left kan extension to compute equalizers for Diagram{op}
Universal property of coequalizers (id) / equalizers (op).

Caveats:

Code for (co)limits of FinCats is stored in Limits.jl to avoid circular dependency. Tests are still in test/.../FinCats.jl
For simplicity, FinCatPresentations are treated (but, ideally, code generically would work with FinCatGraphs as well)
Because of the makeshift way dynamic acsets are implemented, rather than MyCSetType() it's safer to use Base.invokelatest(MyCSetType)
Rebasing on master included a bunch of unrelated commits for some reason. The relevant files are Chase.jl, Limits.jl, CSets.jl, Diagrams.jl.
Left kan extensions are abysmally slow (possibly in large part due to the dynamic acset hack)

fixes and tests remove bad test

…patch-1 add hash method for diagram/diagram hom

…ts-benchmarks Benchmarks for paper

Replace half-baked function `roottype` with `Base.typename`

@inbounds

ENH: removed dynamic allocation of named tuple in rem_part! ENH: sprinkled in some happy little @inbounds ENH: use a named tuple instead of keyword arguments ENH: added ability to preallocate indices for acsets ENH: added search algorithms ENH: set_subpart returns subpart ENH: inbounds for set_subpart ENH: added random graph generators ENH: added faster connected component implementation using bfs ENH: added normalize_labeling function to FinSets ENH: more graph functions BENCH: more benchmarks ENH: benchmark plotting FIX: added back keyword arguments to add_edge! FIX: graph generators shouldn't preallocate to be generic CLEANUP: Replace `normalize_labels` with inline function calls. TEST: added tests for graph generators and searching algorithms DOC: added clarifying comment for add_parts_with_indices! TEST: added tests for degree add hash method for diagram/diagram hom add tests CLEANUP: Use `Base.typename` instead of homemade function `roottype`.

Substituting syms and inverting wiring diagrams Allow vertex coloring, catlab theory to EqTheory conversion Invert diagram fixed for passwires Split chase into parts, simpler trim function, many functions which depended on EqTheory but really just needed the theory's generators have been updated to reflect this bugfix remove wiring diagram interface Removed code is now in GraphicalLinearAlgebra.jl

extend_morphism

fixes and tests remove bad test

- FinTransformationMap (between FinFunctors to Set) <-> ACSetTransformation - naturality of DiagramHoms - currying of fintransformationmap - fix bug in coequalizer of fincats

explained example of a pushout in diag(Grph)

kris-brown · 2022-04-12T23:18:51Z

cleaned up commit history and resubmit as #615

kris-brown and others added 30 commits March 18, 2022 12:51

(co)products/(co)equalizers for Fincats and Diagrams

7a320b2

fixes and tests remove bad test

universal for FinCat (co)limits

4711108

Universal properties of (co)products for fincats/diagrams

7626855

equalizer universal property for diagrams

0e712e4

ENH: made copy into a compile-time parameter for incident

190f62b

ENH: removed dynamic allocation of named tuple in rem_part!

e1b92ea

ENH: sprinkled in some happy little @inbounds

86b5736

ENH: use a named tuple instead of keyword arguments

ce19360

ENH: added ability to preallocate indices for acsets

3bdcb84

ENH: added search algorithms

2a77689

ENH: set_subpart returns subpart

4c892d5

ENH: inbounds for set_subpart

1f4d53a

ENH: added random graph generators

a679cc6

ENH: added faster connected component implementation using bfs

1ae04db

ENH: added normalize_labeling function to FinSets

12dbd8f

ENH: more graph functions

abc5b9b

BENCH: more benchmarks

4138f6d

ENH: benchmark plotting

6fa05e4

FIX: added back keyword arguments to add_edge!

f04b68e

FIX: graph generators shouldn't preallocate to be generic

5affdcf

CLEANUP: Replace normalize_labels with inline function calls.

fbb56e4

TEST: added tests for graph generators and searching algorithms

5438de6

DOC: added clarifying comment for add_parts_with_indices!

687d273

TEST: added tests for degree

c526f13

add hash method for diagram/diagram hom

92e2d40

add tests

d908a1d

Merge pull request AlgebraicJulia#610 from AlgebraicJulia/kris-brown-…

c964d26

…patch-1 add hash method for diagram/diagram hom

Merge pull request AlgebraicJulia#588 from AlgebraicJulia/struct-acse…

2180056

…ts-benchmarks Benchmarks for paper

CLEANUP: Use Base.typename instead of homemade function roottype.

81ce2d7

Merge pull request AlgebraicJulia#611 from epatters/fix-root-type-of

bb7b81e

Replace half-baked function `roottype` with `Base.typename`

epatters and others added 15 commits March 31, 2022 21:36

BUILD: Release Catlab v0.13.8.

35cb13b

curry/uncurry

cbe30ee

replace copairs with oplus/copair, return a morphism from chase

1e084e7

extend_morphism

C-Rel/C-Set conversion, distinguish EGDs/TGDs, optionally chase in C-Rel

2d4d690

(co)products/(co)equalizers for Fincats and Diagrams

697e18c

fixes and tests remove bad test

universal for FinCat (co)limits

7e859be

Universal properties of (co)products for fincats/diagrams

289a47f

equalizer universal property for diagrams

378249e

Start ob/hom generalization but not far into it, saving progress

2c860e7

parameterized chase by ob/hom

44ad4df

Merge branch 'curry_adj' into category_of_diagrams

8a3eadf

left kan extensions. equations in (co)product of fincats.

5a798c8

remove revise

0bb2482

kris-brown mentioned this pull request Apr 5, 2022

Pushout based chase #512

Closed

kris-brown added 4 commits April 5, 2022 11:52

Left Kan returns natural transformation too / allow eqs in ACSetFunctor

846bc27

Left kan universal property

c10c78d

hash for Presentation, leftkan in Diagrams.jl, coeq of DiagramHoms{id}

c523aae

- FinTransformationMap (between FinFunctors to Set) <-> ACSetTransformation - naturality of DiagramHoms - currying of fintransformationmap - fix bug in coequalizer of fincats

fixed universal prop of leftkan, verbose is_natural

4e1cf10

explained example of a pushout in diag(Grph)

kris-brown closed this Apr 12, 2022

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(co)products/(co)equalizers for Fincats and Diagrams #609

(co)products/(co)equalizers for Fincats and Diagrams #609

kris-brown commented Mar 18, 2022 •

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kris-brown commented Apr 12, 2022

(co)products/(co)equalizers for Fincats and Diagrams #609

(co)products/(co)equalizers for Fincats and Diagrams #609

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kris-brown commented Mar 18, 2022 •

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