Edit Profile (opens in new tab) Garner, Richard Co-Author Distance Author ID: garner.richard Published as: Garner, Richard Homepage: http://web.science.mq.edu.au/~rgarner/ External Links: MGP · ORCID · Wikidata · dblp Documents Indexed: 56 Publications since 2006 1 Contribution as Editor · 1 Further Contribution Co-Authors: 31 Co-Authors with 34 Joint Publications 441 Co-Co-Authors all top 5 Co-Authors 24 single-authored 5 Bourke, John 5 Lack, Stephen 3 Van den Berg, Benno 2 Awodey, Steve 2 Buckley, Mitchell 2 Cockett, J. Robin B. 2 Curien, Pierre-Louis 2 Gambino, Nicola 2 Hirschowitz, Tom 2 Hofmann, Martin 2 Kock, Joachim 2 Martin-Löf, Per 2 Riehl, Emily 2 Shulman, Michael A. 2 Street, Ross H. 2 Voevodskiĭ, Vladimir Aleksandrovich 2 Weber, Mark 1 Aczel, Peter 1 Ahrens, Benedikt 1 Altenkirch, Thorsten 1 Angiuli, Carlo 1 Avigad, Jeremy 1 Balchin, Scott 1 Barras, Bruno 1 Bauer, Andrej 1 Bertot, Yves 1 Bezem, Marc 1 Bordg, Anthony 1 Brunerie, Guillaume 1 Cohen, Cyril 1 Constable, Robert Lee 1 Coquand, Thierry 1 Dybjer, Peter 1 Feller, Matthew 1 Finster, Eric 1 Gonthier, Georges 1 Grayson, Daniel Richard 1 Gurski, Nick 1 Hales, Thomas Callister 1 Harper, Robert 1 Herbelin, Hugo 1 Hofstra, Pieter J. W. 1 Hötzel Escardó, Martín 1 Hou (Favonia), Kuen-Bang 1 Joachim, Kock 1 Joyal, André 1 Kapulkin, Krzysztof 1 Kȩdziorek, Magdalena 1 Kraus, Nicolai 1 Li, Nuo 1 Licata, Dan 1 Lin, Daniel W. 1 López Franco, Ignacio L. 1 Lumsdaine, Peter LeFanu 1 Luo, Zhaohui 1 Mahboubi, Assia 1 Melikhov, Sergey Aleksandrovich 1 Nahas, Michael 1 Pacaud Lemay, Jean-Simon 1 Palmgren, Erik 1 Pardon, Aurélien 1 Pelayo, Alvaro 1 Polonsky, Andrew 1 Power, John 1 Proulx, May U. 1 Rijke, Egbert 1 Schäppi, Daniel 1 Scott, Dana Stewart 1 Scott, Philip J. 1 Slevin, Paul 1 Sojakova, Kristina 1 Solov’ëv, Sergeĭ Vladimirovich 1 Sozeau, Matthieu 1 Spitters, Bas 1 Streicher, Thomas 1 1 Warren, Michael Alton 1 Zeilberger, Noam all top 5 Serials 10 Journal of Pure and Applied Algebra 9 Advances in Mathematics 6 Applied Categorical Structures 6 Theory and Applications of Categories 4 Mathematical Proceedings of the Cambridge Philosophical Society 3 Theoretical Computer Science 2 Annals of Pure and Applied Logic 2 Journal of Logic and Computation 2 MSCS. Mathematical Structures in Computer Science 2 Logical Methods in Computer Science 1 Journal of Algebra 1 Proceedings of the London Mathematical Society. Third Series 1 Information and Computation 1 Bulletin of the Belgian Mathematical Society - Simon Stevin 1 Communications in Contemporary Mathematics 1 Cahiers de Topologie et Géométrie Différentielle Catégoriques 1 ACM Transactions on Computational Logic 1 Oberwolfach Reports 1 Journal of Topology 1 Annals of \(K\)-Theory all top 5 Fields 53 Category theory; homological algebra (18-XX) 12 Algebraic topology (55-XX) 10 Mathematical logic and foundations (03-XX) 6 Computer science (68-XX) 2 Combinatorics (05-XX) 2 Associative rings and algebras (16-XX) 2 Group theory and generalizations (20-XX) 2 General topology (54-XX) 1 General and overarching topics; collections (00-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 General algebraic systems (08-XX) 1 \(K\)-theory (19-XX) 1 Topological groups, Lie groups (22-XX) 1 Global analysis, analysis on manifolds (58-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 48 Publications have been cited 372 times in 258 Documents Cited by ▼ Year ▼ Homotopy type theory. Univalent foundations of mathematics. Zbl 1298.03002The Univalent Foundations Program 128 2013 Understanding the small object argument. Zbl 1173.55009Garner, Richard 46 2009 The identity type weak factorisation system. Zbl 1157.68022Gambino, Nicola; Garner, Richard 33 2008 Types are weak \(\omega \)-groupoids. Zbl 1229.18007van den Berg, Benno; Garner, Richard 27 2011 Algebraic weak factorisation systems. I: Accessible AWFS. Zbl 1327.18004Bourke, John; Garner, Richard 23 2016 Topological and simplicial models of identity types. Zbl 1352.03012van den Berg, Benno; Garner, Richard 21 2012 Enriched categories as a free cocompletion. Zbl 1334.18004Garner, Richard; Shulman, Michael 16 2016 The low-dimensional structures formed by tricategories. Zbl 1169.18001Garner, Richard; Gurski, Nick 13 2009 Two-dimensional models of type theory. Zbl 1230.03043Garner, Richard 12 2009 Lifting accessible model structures. Zbl 1442.18011Garner, Richard; Kędziorek, Magdalena; Riehl, Emily 12 2020 The Catalan simplicial set. Zbl 1376.18005Buckley, Mitchell; Garner, Richard; Lack, Stephen; Street, Ross 11 2015 On the axioms for adhesive and quasiadhesive categories. Zbl 1248.18001Garner, Richard; Lack, Stephen 11 2012 Homomorphisms of higher categories. Zbl 1205.18004Garner, Richard 9 2010 Algebraic weak factorisation systems. II: Categories of weak maps. Zbl 1327.18005Bourke, John; Garner, Richard 9 2016 Revisiting the categorical interpretation of dependent type theory. Zbl 1433.03029Curien, Pierre-Louis; Garner, Richard; Hofmann, Martin 8 2014 Lex colimits. Zbl 1256.18002Garner, Richard; Lack, Stephen 8 2012 On the strength of dependent products in the type theory of Martin-Löf. Zbl 1171.03004Garner, Richard 8 2009 Polycategories via pseudo-distributive laws. Zbl 1146.18002Garner, Richard 8 2008 On semiflexible, flexible and pie algebras. Zbl 1280.18003Bourke, John; Garner, Richard 7 2013 Two-dimensional regularity and exactness. Zbl 1298.18005Bourke, John; Garner, Richard 7 2014 Every \(2\)-Segal space is unital. Zbl 1452.18027Feller, Matthew; Garner, Richard; Joachim, Kock; Proulx, May U.; Weber, Mark 7 2021 Restriction categories as enriched categories. Zbl 1288.18007Cockett, Robin; Garner, Richard 6 2014 Monads and theories. Zbl 1434.18003Bourke, John; Garner, Richard 6 2019 A homotopy-theoretic universal property of Leinster’s operad for weak \(\omega \)-categories. Zbl 1188.18006Garner, Richard 6 2009 Topological functors as total categories. Zbl 1305.18005Garner, Richard 5 2014 Lawvere theories, finitary monads and Cauchy-completion. Zbl 1329.18008Garner, Richard 5 2014 Double clubs. Zbl 1117.18003Garner, Richard 5 2006 An embedding theorem for tangent categories. Zbl 1430.18007Garner, Richard 4 2018 Commutativity. Zbl 1375.18049Garner, Richard; López Franco, Ignacio 4 2016 The Vietoris monad and weak distributive laws. Zbl 1442.18010Garner, Richard 4 2020 Shapely monads and analytic functors. Zbl 1444.18009Garner, Richard; Hirschowitz, Tom 3 2018 Grothendieck quasitoposes. Zbl 1282.18002Garner, Richard; Lack, Stephen 3 2012 Combinatorial structure of type dependency. Zbl 1369.03096Garner, Richard 2 2015 The Isbell monad. Zbl 1366.18002Garner, Richard 2 2015 When coproducts are biproducts. Zbl 1371.18002Garner, Richard; Schäppi, Daniel 2 2016 A characterisation of algebraic exactness. Zbl 1278.18020Garner, Richard 2 2013 An enriched view on the extended finitary monad-Lawvere theory correspondence. Zbl 1419.18004Garner, Richard; Power, John 2 2018 Mini-workshop: The homotopy interpretation of constructive type theory. Abstracts from the mini-workshop held February 27th-March 05th, 2011. Zbl 1242.00037 2 2011 Understanding the small object argument. Zbl 1256.55005Garner, Richard 2 2012 Cocompletion of restriction categories. Zbl 1441.18005Garner, Richard; Lin, Daniel 2 2020 Cartesian differential categories as skew enriched categories. Zbl 1478.18007Garner, Richard; Lemay, Jean-Simon Pacaud 2 2021 Hochschild homology, lax codescent, and duplicial structure. Zbl 1387.18027Garner, Richard; Lack, Stephen; Slevin, Paul 1 2018 Orientals and cubes, inductively. Zbl 1375.18031Buckley, Mitchell; Garner, Richard 1 2016 Diagrammatic characterisation of enriched absolute colimits. Zbl 1317.18005Garner, Richard 1 2014 Ionads. Zbl 1266.18006Garner, Richard 1 2012 Coalgebras governing both weighted Hurwitz products and their pointwise transforms. Zbl 1372.18007Garner, Richard; Street, Ross 1 2016 Bousfield localisation and colocalisation of one-dimensional model structures. Zbl 1416.55004Balchin, Scott; Garner, Richard 1 2019 The costructure-cosemantics adjunction for comodels for computational effects. Zbl 1506.68051Garner, Richard 1 2022 The costructure-cosemantics adjunction for comodels for computational effects. Zbl 1506.68051Garner, Richard 1 2022 Every \(2\)-Segal space is unital. Zbl 1452.18027Feller, Matthew; Garner, Richard; Joachim, Kock; Proulx, May U.; Weber, Mark 7 2021 Cartesian differential categories as skew enriched categories. Zbl 1478.18007Garner, Richard; Lemay, Jean-Simon Pacaud 2 2021 Lifting accessible model structures. Zbl 1442.18011Garner, Richard; Kędziorek, Magdalena; Riehl, Emily 12 2020 The Vietoris monad and weak distributive laws. Zbl 1442.18010Garner, Richard 4 2020 Cocompletion of restriction categories. Zbl 1441.18005Garner, Richard; Lin, Daniel 2 2020 Monads and theories. Zbl 1434.18003Bourke, John; Garner, Richard 6 2019 Bousfield localisation and colocalisation of one-dimensional model structures. Zbl 1416.55004Balchin, Scott; Garner, Richard 1 2019 An embedding theorem for tangent categories. Zbl 1430.18007Garner, Richard 4 2018 Shapely monads and analytic functors. Zbl 1444.18009Garner, Richard; Hirschowitz, Tom 3 2018 An enriched view on the extended finitary monad-Lawvere theory correspondence. Zbl 1419.18004Garner, Richard; Power, John 2 2018 Hochschild homology, lax codescent, and duplicial structure. Zbl 1387.18027Garner, Richard; Lack, Stephen; Slevin, Paul 1 2018 Algebraic weak factorisation systems. I: Accessible AWFS. Zbl 1327.18004Bourke, John; Garner, Richard 23 2016 Enriched categories as a free cocompletion. Zbl 1334.18004Garner, Richard; Shulman, Michael 16 2016 Algebraic weak factorisation systems. II: Categories of weak maps. Zbl 1327.18005Bourke, John; Garner, Richard 9 2016 Commutativity. Zbl 1375.18049Garner, Richard; López Franco, Ignacio 4 2016 When coproducts are biproducts. Zbl 1371.18002Garner, Richard; Schäppi, Daniel 2 2016 Orientals and cubes, inductively. Zbl 1375.18031Buckley, Mitchell; Garner, Richard 1 2016 Coalgebras governing both weighted Hurwitz products and their pointwise transforms. Zbl 1372.18007Garner, Richard; Street, Ross 1 2016 The Catalan simplicial set. Zbl 1376.18005Buckley, Mitchell; Garner, Richard; Lack, Stephen; Street, Ross 11 2015 Combinatorial structure of type dependency. Zbl 1369.03096Garner, Richard 2 2015 The Isbell monad. Zbl 1366.18002Garner, Richard 2 2015 Revisiting the categorical interpretation of dependent type theory. Zbl 1433.03029Curien, Pierre-Louis; Garner, Richard; Hofmann, Martin 8 2014 Two-dimensional regularity and exactness. Zbl 1298.18005Bourke, John; Garner, Richard 7 2014 Restriction categories as enriched categories. Zbl 1288.18007Cockett, Robin; Garner, Richard 6 2014 Topological functors as total categories. Zbl 1305.18005Garner, Richard 5 2014 Lawvere theories, finitary monads and Cauchy-completion. Zbl 1329.18008Garner, Richard 5 2014 Diagrammatic characterisation of enriched absolute colimits. Zbl 1317.18005Garner, Richard 1 2014 Homotopy type theory. Univalent foundations of mathematics. Zbl 1298.03002The Univalent Foundations Program 128 2013 On semiflexible, flexible and pie algebras. Zbl 1280.18003Bourke, John; Garner, Richard 7 2013 A characterisation of algebraic exactness. Zbl 1278.18020Garner, Richard 2 2013 Topological and simplicial models of identity types. Zbl 1352.03012van den Berg, Benno; Garner, Richard 21 2012 On the axioms for adhesive and quasiadhesive categories. Zbl 1248.18001Garner, Richard; Lack, Stephen 11 2012 Lex colimits. Zbl 1256.18002Garner, Richard; Lack, Stephen 8 2012 Grothendieck quasitoposes. Zbl 1282.18002Garner, Richard; Lack, Stephen 3 2012 Understanding the small object argument. Zbl 1256.55005Garner, Richard 2 2012 Ionads. Zbl 1266.18006Garner, Richard 1 2012 Types are weak \(\omega \)-groupoids. Zbl 1229.18007van den Berg, Benno; Garner, Richard 27 2011 Mini-workshop: The homotopy interpretation of constructive type theory. Abstracts from the mini-workshop held February 27th-March 05th, 2011. Zbl 1242.00037 2 2011 Homomorphisms of higher categories. Zbl 1205.18004Garner, Richard 9 2010 Understanding the small object argument. Zbl 1173.55009Garner, Richard 46 2009 The low-dimensional structures formed by tricategories. Zbl 1169.18001Garner, Richard; Gurski, Nick 13 2009 Two-dimensional models of type theory. Zbl 1230.03043Garner, Richard 12 2009 On the strength of dependent products in the type theory of Martin-Löf. Zbl 1171.03004Garner, Richard 8 2009 A homotopy-theoretic universal property of Leinster’s operad for weak \(\omega \)-categories. Zbl 1188.18006Garner, Richard 6 2009 The identity type weak factorisation system. Zbl 1157.68022Gambino, Nicola; Garner, Richard 33 2008 Polycategories via pseudo-distributive laws. Zbl 1146.18002Garner, Richard 8 2008 Double clubs. Zbl 1117.18003Garner, Richard 5 2006 all cited Publications top 5 cited Publications all top 5 Cited by 273 Authors 22 Garner, Richard 10 Bourke, John 8 Lumsdaine, Peter LeFanu 8 Shulman, Michael A. 7 Kapulkin, Krzysztof 7 Lack, Stephen 7 Riehl, Emily 6 Awodey, Steve 6 Gambino, Nicola 6 Veltri, Niccolò 5 López Franco, Ignacio L. 5 Lucyshyn-Wright, Rory B. B. 5 Rosický, Jiří 5 Uustalu, Tarmo 4 Hackney, Philip 4 Harper, Robert 4 Kock, Joachim 4 Osorno, Angélica Maria 4 Rovelli, Martina 4 Spivak, David I. 4 Tholen, Walter 4 Warren, Michael Alton 4 Zeilberger, Noam 3 Angiuli, Carlo 3 Behr, Nicolas 3 Bonchi, Filippo 3 Campbell, Alexander Peter 3 Cegarra, Antonio Martínez 3 Clementino, Maria Manuel 3 Cockett, J. Robin B. 3 Cottrell, Thomas 3 Di Liberti, Ivan 3 Endrullis, Jörg 3 Fujii, Soichiro 3 Gurski, Nick 3 Henry, Simon 3 Hirschowitz, Tom 3 North, Paige Randall 3 Ozornova, Viktoriya 3 Pronk, Dorette A. 3 Rosset, Aloïs 3 Street, Ross H. 3 Velebil, Jiří 2 Adámek, Jiří 2 Aravantinos-Sotiropoulos, Vasileios 2 Axelsen, Holger Bock 2 Balchin, Scott 2 Bergner, Julie 2 Bezem, Marc 2 Böhm, Gabriella 2 Buckley, Mitchell 2 Carrasco, Pilar C. 2 Chu, Hongyi 2 Coquand, Thierry 2 Cruttwell, G. S. H. 2 Cruttwell, Geoff 2 Dostál, Matěj 2 Dybjer, Peter 2 Eberhart, Clovis 2 Emmenegger, Jacopo 2 Gallagher, Jonathan 2 Garzón, Antonio R. 2 Gaucher, Philippe 2 Grandis, Marco 2 Harmer, Russ 2 Harper, John E. 2 Haugseng, Rune 2 Hofstra, Pieter J. W. 2 Hötzel Escardó, Martín 2 Jacqmin, Pierre-Alain 2 Kaarsgaard, Robin 2 Klev, Ansten Mørch 2 Kosiol, Jens 2 Krivine, Jean 2 Licata, Daniel R. 2 Lobbia, Gabriele 2 Loregiàn, Fosco 2 Orton, Ian 2 Overbeek, Roy 2 Pasquali, Fabio 2 Pitts, Andrew M. 2 Power, John 2 Rosolini, Giuseppe 2 Santamaria, Alessio 2 Scheimbauer, Claudia I. 2 Shen, Lili 2 Sobociński, Paweł 2 Stroiński, Mateusz 2 Taentzer, Gabriele 2 Tendas, Giacomo 2 Uemura, Taichi 2 Van den Berg, Benno 2 van der Weide, Niels 2 van Oosten, Jaap 2 Vasilakopoulou, Christina 2 Voevodskiĭ, Vladimir Aleksandrovich 2 Wisnesky, Ryan 2 Yau, Donald Y. 1 Aguiar, Marcelo 1 Ahrens, Benedikt ...and 173 more Authors all top 5 Cited in 59 Serials 29 Journal of Pure and Applied Algebra 26 Applied Categorical Structures 24 Advances in Mathematics 22 MSCS. Mathematical Structures in Computer Science 20 Theory and Applications of Categories 13 Logical Methods in Computer Science 7 Annals of Pure and Applied Logic 6 Algebraic & Geometric Topology 5 Higher Structures 4 Topology and its Applications 4 Journal of Homotopy and Related Structures 4 Journal of Logical and Algebraic Methods in Programming 3 Journal of the London Mathematical Society. Second Series 3 The New York Journal of Mathematics 3 Categories and General Algebraic Structures with Applications 2 Journal of Algebra 2 The Journal of Symbolic Logic 2 Proceedings of the American Mathematical Society 2 Theoretical Computer Science 2 Transactions of the American Mathematical Society 2 Journal of Automated Reasoning 2 Indagationes Mathematicae. New Series 2 Topoi 1 Bulletin of the Australian Mathematical Society 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Russian Mathematical Surveys 1 Reviews in Mathematical Physics 1 Bulletin of the London Mathematical Society 1 Compositio Mathematica 1 Mathematica Scandinavica 1 Mathematische Zeitschrift 1 Memoirs of the American Mathematical Society 1 Publications de l’Institut Mathématique. Nouvelle Série 1 Advances in Applied Mathematics 1 Extracta Mathematicae 1 Forum Mathematicum 1 Bulletin of the American Mathematical Society. New Series 1 Expositiones Mathematicae 1 Journal of Functional Programming 1 Selecta Mathematica. New Series 1 The Bulletin of Symbolic Logic 1 Geometry & Topology 1 Algebras and Representation Theory 1 Journal of the European Mathematical Society (JEMS) 1 Cahiers de Topologie et Géométrie Différentielle Catégoriques 1 Journal of the Institute of Mathematics of Jussieu 1 ACM Transactions on Computational Logic 1 Journal of Applied Logic 1 Mediterranean Journal of Mathematics 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Logica Universalis 1 Tbilisi Mathematical Journal 1 Journal of \(K\)-Theory 1 Journal of Logic and Analysis 1 Applied General Topology 1 Forum of Mathematics, Sigma 1 Mathematics 1 Annals of \(K\)-Theory 1 La Matematica all top 5 Cited in 25 Fields 202 Category theory; homological algebra (18-XX) 90 Algebraic topology (55-XX) 81 Mathematical logic and foundations (03-XX) 45 Computer science (68-XX) 17 Associative rings and algebras (16-XX) 12 Order, lattices, ordered algebraic structures (06-XX) 8 General algebraic systems (08-XX) 7 \(K\)-theory (19-XX) 6 Group theory and generalizations (20-XX) 6 General topology (54-XX) 5 Quantum theory (81-XX) 4 Manifolds and cell complexes (57-XX) 3 Commutative algebra (13-XX) 3 Nonassociative rings and algebras (17-XX) 2 Combinatorics (05-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Field theory and polynomials (12-XX) 1 Algebraic geometry (14-XX) 1 Topological groups, Lie groups (22-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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