Refactor & Simplify AlgebroidsFromDataTables using FpCategories

[kamalsaleh]

plus few tweaks here and there.

[kamalsaleh]

Of course, let me know when you have time

[codecov[bot]]

Codecov Report

Attention: 16 lines in your changes are missing coverage. Please review.

Comparison is base (63d25cb) 75.50% compared to head (c9aa0f6) 75.42%.

Files	Patch %	Lines
.../FunctionalPreSheavesOfAlgebroidsFromDataTables.gi	95.58%	11 Missing :warning:
...tiveClosureOfAlgebroidFromDataTablesPrecompiled.gi	97.24%	4 Missing :warning:
...LinearClosuresOfPathCategoriesAndTheirQuotients.gi	92.85%	1 Missing :warning:

Additional details and impacted files

```diff @@ Coverage Diff @@ ## master #434 +/- ## ========================================== - Coverage 75.50% 75.42% -0.09% ========================================== Files 376 377 +1 Lines 55967 55819 -148 ========================================== - Hits 42260 42103 -157 - Misses 13707 13716 +9 ``` | [Flag](https://app.codecov.io/gh/homalg-project/CategoricalTowers/pull/434/flags?src=pr&el=flags&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=homalg-project) | Coverage Δ | | |---|---|---| | [Algebroids](https://app.codecov.io/gh/homalg-project/CategoricalTowers/pull/434/flags?src=pr&el=flag&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=homalg-project) | `75.76% <96.57%> (-0.36%)` | :arrow_down: | | [CatReps](https://app.codecov.io/gh/homalg-project/CategoricalTowers/pull/434/flags?src=pr&el=flag&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=homalg-project) | `83.16% <ø> (ø)` | | | [CategoriesWithAmbientObjects](https://app.codecov.io/gh/homalg-project/CategoricalTowers/pull/434/flags?src=pr&el=flag&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=homalg-project) | `89.30% <ø> (ø)` | | | [ExteriorPowersCategories](https://app.codecov.io/gh/homalg-project/CategoricalTowers/pull/434/flags?src=pr&el=flag&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=homalg-project) | `43.70% <ø> (ø)` | | | [FiniteCocompletions](https://app.codecov.io/gh/homalg-project/CategoricalTowers/pull/434/flags?src=pr&el=flag&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=homalg-project) | `91.94% <ø> (ø)` | | | [FpCategories](https://app.codecov.io/gh/homalg-project/CategoricalTowers/pull/434/flags?src=pr&el=flag&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=homalg-project) | `86.10% <98.82%> (+0.04%)` | :arrow_up: | | [FunctorCategories](https://app.codecov.io/gh/homalg-project/CategoricalTowers/pull/434/flags?src=pr&el=flag&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=homalg-project) | `64.49% <100.00%> (ø)` | | | [GradedCategories](https://app.codecov.io/gh/homalg-project/CategoricalTowers/pull/434/flags?src=pr&el=flag&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=homalg-project) | `86.57% <ø> (ø)` | | | [InternalModules](https://app.codecov.io/gh/homalg-project/CategoricalTowers/pull/434/flags?src=pr&el=flag&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=homalg-project) | `81.66% <ø> (ø)` | | | [IntrinsicCategories](https://app.codecov.io/gh/homalg-project/CategoricalTowers/pull/434/flags?src=pr&el=flag&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=homalg-project) | `82.57% <ø> (ø)` | | | [IntrinsicGradedModules](https://app.codecov.io/gh/homalg-project/CategoricalTowers/pull/434/flags?src=pr&el=flag&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=homalg-project) | `50.89% <ø> (ø)` | | | [IntrinsicModules](https://app.codecov.io/gh/homalg-project/CategoricalTowers/pull/434/flags?src=pr&el=flag&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=homalg-project) | `82.15% <ø> (ø)` | | | [LazyCategories](https://app.codecov.io/gh/homalg-project/CategoricalTowers/pull/434/flags?src=pr&el=flag&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=homalg-project) | `74.20% <ø> (ø)` | | | [Locales](https://app.codecov.io/gh/homalg-project/CategoricalTowers/pull/434/flags?src=pr&el=flag&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=homalg-project) | `85.44% <ø> (ø)` | | | [PreSheaves](https://app.codecov.io/gh/homalg-project/CategoricalTowers/pull/434/flags?src=pr&el=flag&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=homalg-project) | `92.42% <ø> (ø)` | | | [QuotientCategories](https://app.codecov.io/gh/homalg-project/CategoricalTowers/pull/434/flags?src=pr&el=flag&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=homalg-project) | `91.58% <ø> (ø)` | | | [SubcategoriesForCAP](https://app.codecov.io/gh/homalg-project/CategoricalTowers/pull/434/flags?src=pr&el=flag&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=homalg-project) | `81.32% <ø> (ø)` | | | [ToolsForCategoricalTowers](https://app.codecov.io/gh/homalg-project/CategoricalTowers/pull/434/flags?src=pr&el=flag&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=homalg-project) | `82.82% <ø> (ø)` | | | [Toposes](https://app.codecov.io/gh/homalg-project/CategoricalTowers/pull/434/flags?src=pr&el=flag&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=homalg-project) | `90.26% <ø> (ø)` | | | [ZariskiFrames](https://app.codecov.io/gh/homalg-project/CategoricalTowers/pull/434/flags?src=pr&el=flag&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=homalg-project) | `74.31% <ø> (ø)` | | Flags with carried forward coverage won't be shown. [Click here](https://docs.codecov.io/docs/carryforward-flags?utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=homalg-project#carryforward-flags-in-the-pull-request-comment) to find out more.

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[mohamed-barakat]

Thanks.