From mboxrd@z Thu Jan 1 00:00:00 1970 X-Received: by 10.13.254.198 with SMTP id o189mr16053682ywf.62.1497970701038; Tue, 20 Jun 2017 07:58:21 -0700 (PDT) X-BeenThere: homotopytypetheory@googlegroups.com Received: by 10.36.211.144 with SMTP id n138ls601055itg.11.gmail; Tue, 20 Jun 2017 07:58:19 -0700 (PDT) X-Received: by 10.99.227.85 with SMTP id o21mr14820747pgj.20.1497970699918; Tue, 20 Jun 2017 07:58:19 -0700 (PDT) ARC-Seal: i=1; a=rsa-sha256; t=1497970699; cv=none; d=google.com; s=arc-20160816; b=oRjYGn4HPBjMJumnqfbJbn1dhf7aD5UMo5QOPR009GXBf77aw00rPDeUvTDFq7haFT Rj6w5RskBvf5vZexXIIzdhY8tFDZswxmNWE1m/TQObpie1Vd7VaSKeFZLnDuR8NdqNGo HaqGd4jHvt6JR/wh6+Gx3zp8GosczgUBIs8Q+MAV4Cd8dcWMA0KVAeUOvDB6S2x5aTk/ Oi6RDviuoXkNm4mqDMM9JPHXgtSmeK/CI80tNE6DKsOoOPCqV4N9NHTeOlPfBKufOTZZ 6O8SK/eViXMCibFmCzCasm+xzU2miZH9c00qPMAPDcbS3r1rtKnuAMhDZYqmsfW44jPw slRA== ARC-Message-Signature: i=1; a=rsa-sha256; c=relaxed/relaxed; d=google.com; s=arc-20160816; h=to:subject:message-id:date:from:mime-version:dkim-signature :arc-authentication-results; bh=25ShUGNYy2pnbUZlGjn89CWDTxCZ7jPT8g1+Pzmx4W0=; b=Y6lLmMAvLSgQoiGq+uZxeBT1eU4u8WltdIuJfJECVfWnb6NJOBBfg5DgI1yH8M4RON EdPF3DRZHBDuFNSsAsGQFs2zAwiN78H3e4SpK4KzoHGYxfCEgq3XSXLnHLaOozi0JZ2E 0D1nMLxTEDerVxJuMGGGb/ULTblU7h58V5jmcvvGZwOFh8Z/LI2ps+Y1w7cWXM0Hf6Ft 4m2H8/vrdN4Y9O7maOhZyanSdfPsF688PqNbEFWrWgKVGobzmjkXjiyJgDgPLC3B/Mob 6aeYSosgx2sG/KdTkwsMIZVewJWKrbcjmtE3/X2AxLs77eCUlxrI1orAiSiwTJjrWIv4 G8hw== ARC-Authentication-Results: i=1; gmr-mx.google.com; dkim=pass head...@gmail.com header.b=DwQGcIvU; spf=pass (google.com: domain of andrew....@gmail.com designates 2607:f8b0:400c:c08::22e as permitted sender) smtp.mailfrom=andrew....@gmail.com; dmarc=pass (p=NONE sp=NONE dis=NONE) header.from=gmail.com Return-Path: Received: from mail-ua0-x22e.google.com (mail-ua0-x22e.google.com. [2607:f8b0:400c:c08::22e]) by gmr-mx.google.com with ESMTPS id n1si2408321vke.0.2017.06.20.07.58.19 for (version=TLS1_2 cipher=ECDHE-RSA-AES128-GCM-SHA256 bits=128/128); Tue, 20 Jun 2017 07:58:19 -0700 (PDT) Received-SPF: pass (google.com: domain of andrew....@gmail.com designates 2607:f8b0:400c:c08::22e as permitted sender) client-ip=2607:f8b0:400c:c08::22e; Authentication-Results: gmr-mx.google.com; dkim=pass head...@gmail.com header.b=DwQGcIvU; spf=pass (google.com: domain of andrew....@gmail.com designates 2607:f8b0:400c:c08::22e as permitted sender) smtp.mailfrom=andrew....@gmail.com; dmarc=pass (p=NONE sp=NONE dis=NONE) header.from=gmail.com Received: by mail-ua0-x22e.google.com with SMTP id d45so43585631uai.1 for ; Tue, 20 Jun 2017 07:58:19 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025; h=mime-version:from:date:message-id:subject:to; bh=25ShUGNYy2pnbUZlGjn89CWDTxCZ7jPT8g1+Pzmx4W0=; b=DwQGcIvUI/afP1gqZkhmdnwGglAkdrcxzOKq7ZWiMxZfGadf6nAEFxt9gJhLwzjWxz Ips2l56vWXlGyg02mtaXRKGy3UP6LDf0X7X+MlTvcQKHZN8Lv3F0mNv9lPUPcEG9TEeC oycOz6nTFtieA5XVHFs7QPxXGSOIGSSimHl+88ITWN3ZCn/vC3S2M9eRn2G9x6eBEDS8 tZEM6W+sW/xOAaE6tb7RDrCw5fwMGCo6aZrqNz0Au7Wql4vcNm57Hk7ixPieut8l4i/L NGt6at2PUnJEccfnnHr3ovbfEP9akLwCfrgL0SVX1Q1wbHK5BubXmhJbTPmPjiF7DaeF xSKw== X-Gm-Message-State: AKS2vOx17Znzy4euIplyOJP7BtYmZ3WLRRPtH0vFZ4VFXMJ8MLsOpLMZ YDOUGhRqbbxnACXLoozgOu8RqsHCjdsJ X-Received: by 10.176.68.1 with SMTP id m1mr5994764uam.121.1497970699143; Tue, 20 Jun 2017 07:58:19 -0700 (PDT) MIME-Version: 1.0 Received: by 10.103.149.141 with HTTP; Tue, 20 Jun 2017 07:58:18 -0700 (PDT) From: Andrew Polonsky Date: Tue, 20 Jun 2017 16:58:18 +0200 Message-ID: Subject: Is "classical" Hedberg's Theorem true? To: "HomotopyT...@googlegroups.com" Content-Type: multipart/alternative; boundary="94eb2c06abb86821930552657b6e" --94eb2c06abb86821930552657b6e Content-Type: text/plain; charset="UTF-8" This could be a very interesting question: Does every algebraic theory T with decidable word problem admit a coherent presentation? Here a presentation is "coherent" if it is such when T is considered as a monoidal category. See, for instance @article{DBLP:journals/corr/CurienM17, author = {Pierre{-}Louis Curien and Samuel Mimram}, title = {Coherent Presentations of Monoidal Categories}, journal = {CoRR}, volume = {abs/1705.03553}, year = {2017}, url = {http://arxiv.org/abs/1705.03553}, timestamp = {Wed, 07 Jun 2017 14:42:32 +0200}, biburl = {http://dblp.uni-trier.de/rec/bib/journals/corr/CurienM17}, bibsource = {dblp computer science bibliography, http://dblp.org} } Cheers, Andrew --94eb2c06abb86821930552657b6e Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable
This could be a very interesting question:
=
Does every algebraic theory T with decidable word problem ad= mit a coherent presentation?

Here a presentation i= s "coherent" if it is such when T is considered as a monoidal cat= egory.=C2=A0 See, for instance

@article{DBLP:= journals/corr/CurienM17,
=C2=A0 author =C2=A0 =C2=A0=3D {Pierre{-= }Louis Curien and
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2= =A0 =C2=A0Samuel Mimram},
=C2=A0 title =C2=A0 =C2=A0 =3D {Coheren= t Presentations of Monoidal Categories},
=C2=A0 journal =C2=A0 = =3D {CoRR},
=C2=A0 volume =C2=A0 =C2=A0=3D {abs/1705.03553},
=C2=A0 year =C2=A0 =C2=A0 =C2=A0=3D {2017},
=C2=A0 url =C2= =A0 =C2=A0 =C2=A0 =3D {http://a= rxiv.org/abs/1705.03553},
=C2=A0 timestamp =3D {Wed, 07 Jun 2= 017 14:42:32 +0200},
=C2=A0 bibsource =3D= {dblp computer science bibliography, http://db= lp.org}
}

Cheers,
An= drew
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