Proph https://gitlab.com/1337777/cartier/blob/master/cartierSolution.v

solves some question of Cartier which is how to program grammatical meta (metafunctors) ... This starting lemma of polymorph mathematics ( "categories" ) : Coreflections( Set , Funtors( op C , Prop ) ) <=> Funtors( C , Set ) says that the senses ( "metafunctors models" ) onfrom some given primitive-syntax graph may be instead dually viewed as senses ( "coreflective-metafunctors models" ) into some more-complete metafunctors-grammar ( "classifying topos" ). And this starting lemma may be upgraded such to perceive flat metafunctors via geometric morphisms into this metafunctors-grammar. Also this starting lemma may be upgraded such to perceive continuous flat metafunctors via geometric morphisms into some sheaf metafunctors-grammar ... The question is whether these new more-complete metafunctors-grammars are relatively computational/decidable ? This COQ text solves half of this question, the resting half is promised only ... Outline: Primo, the things shall be confined to some meta regular cardinal, and this COQ text assumes-as-axiom some maximum operation inside this regular cardinal and this COQ text assumes-as-axiom some functional extensionality of families of morphisms which are confined to this regular cardinal. Secondo, as was done in the earlier COQ text for colimits, one shall erase/extract some logical cocone-conditions by assuming some erasure/extraction scheme as axiom instead of some very-complicated-induction scheme (beyond induction-induction) ... Tertio, the degradation lemma is more technical than in the earlier COQ texts, because for the congruent-reduction from the copairing operation applied onto some cocone of morphisms, one shall require simultaneous full-reduction of every reductible morphism in the cocone. Most of this COQ program and deduction is automated. Keywords: 1337777.OOO//cartierSolution.v ; metafunctors-grammar ; duality ; classifying topos ----- Memo : The 1337777.OOO SOLUTION PROGRAMME originates from some random-moment discovery of some convergence of the DOSEN PROGRAMME [[http://www.mi.sanu.ac.rs/~kosta]] along the COQ PROGRAMME [[https://coq.inria.fr]]. The 1337777.OOO has discovered [[1337777.OOO//coherence2.v]] [[google.com/#q=1337777.OOO/coherence2.v]] [[https://web.archive.org/web/20170516011054/https://github.com/1337777/dosen/blob/master/coherence2.v]] [fn:4] [fn:5] that the attempt to deduce associative coherence by Maclane is not the reality, because this famous pentagone is in fact some recursive square. This associative coherence is the meta of the semiassociative coherence [[1337777.OOO//coherence.v]] which does lack some more-common Newman-style confluence lemma. Moreover the 1337777.OOO has discovered [[1337777.OOO//borceuxSolution2.v]] [[1337777.OOO//chic05.pdf]] that the "categories" ( "enriched categories" ) only-named by the homologist Maclane are in reality interdependent-cyclic with the natural polymorphism of the logic of Gentzen, this enables some programming of congruent resolution by cut-elimination [[1337777.OOO//dosenSolution3.v]] which will serve as specification (reflection) technique to semi-decide the questions of coherence, in comparasion from the ssreflect-style. Furthermore the 1337777.OOO has discovered [[1337777.OOO//aignerSolution.v]] [[1337777.OOO//ocic04-where-is-combinatorics.pdf]] that the Galois-action for the resolution-modulo ( "symmetry groupoid action" ), is in fact some instance of polymorph functors. And the 1337777.OOO has discovered [[1337777.OOO//ocic03-what-is-normal.djvu]] [[1337777.OOO//laoziSolution2.v]] how to program polymorph coparametrism functors ( "comonad" ). And the 1337777.OOO has discovered [[1337777.OOO//chuSolution.v]] how to program contextual limits of polymorph functors ( "Kan extension" ). And the 1337777.OOO has discovered [[1337777.OOO//cartierSolution.v]] how to program the metafunctors-grammar ( "topos" ), as the primo step towards the programming of the ( "classifying-topos" ) sheaf-metafunctors-grammar which is held as augmented-syntax in the Diaconescu duality lemma ( "coreflective-metafunctors models" ). Another further step shall be to GAP-and-COQ program [[https://www.gap-system.org]] the computational logic for Tarski's decidability in free groups and for convergence in infinite groups ... Additionnally, the 1337777.OOO has discovered random dia-para-logic discoveries [[1337777.OOO//1337777solution.txt]] and information-technology [[1337777.OOO//init.html]] [[1337777.OOO//init.pdf]] [[1337777.OOO//makegit.sh.org]] [[1337777.OOO//editableTree.urp]] [[1337777.OOO//gongji.ml4]] based on the _EMACS org-mode_ logiciel which enables communication of _timed-synchronized_ _geolocated_ _simultaneously-edited_ _multi-authors_ _format-able_ _searchable_ text, and therefore _personal email_ and _public communication_ of _multiple-market/language_ (中文话）textual COQ math programming, and which enables _personal archiving_ and _public archiving_ and therefore _public reviews / webcitations_ . Whatever is discovered, its format, its communication is simultaneously some predictable-time (1337) computational-logical discovery and some random-moment (777) dia-para-computalogical discovery. ----- Memo ( "prealables d'un debat" ) ref the unavoidable question : what is the "ends" / "added-value" / "product" in mathematics ? The "ends" in mathematics are commonly described as "education" and "research". In reality the only "research" ( predictable-time computational-logical discovery, "correct" ) is the engineering of some computational logical computer program or the engineering of some physical prototype, and the rest is "education" ( random-moment dia-para-computalogical discovery, teaching "ideas" ) which is amplified by the question of "audience"/"market" or universality of the communication-language medium [[1337777.OOO//gongji.ml4]]. Unfortunately sometimes forced-fool-and-theft/lie/falsification ( "absence of reality" ) [[1337777.OOO//1337777solution.txt]] defeats both "research" by preventing anything other than " .PDF binary files with pretty greek-letters and large-vertical-symbols ", and defeats "education" by preventing public-review (including public-students review). The medium of this forced-fool-and-theft/lie/falsification may be monetarist or "tribalistic" (interdependent) ... such that it is common ( "maybe half" ) question whether one "tribalistic" (interdependent) teacher's purely predictable-time computational-logical discovery, steals/hides/injects some other original-teacher's "idea" (random-moment dia-para-computalogical discovery) ... and such that it is common ( "maybe half" ) question whether the fabrication/falsification of some non-necessary grade/bounty/reward is precisely to permit "tribalistic" (interdependent) determinism ... or am I the 7ok3r ? ----- paypal 1337777....@gmail.com , wechatpay 2796386...@qq.com , irc #OOO1337777 _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum