Research

Algebras over variable theories, Alg. Univ. 47 (2002), 55-64, with D.B.Benson and M. Necesal

On abstract data types presented by multiequations, Theor. Comp. Sci. 275 (2002), 427-462 , with J.Adámek and M.Hébert

Flat covers and factorizations, J. of Algebra, 253 (2002), 1-13

On a generalized small-object argument for the injective subcategory problem, Cahiers Top. Geom. Diff. Cat. XLIII (2002), 83-106, with J. Adámek, H. Herrlich and W.Tholen

Weak factorization systems and topological functors, Appl. Cat. Str. 10 (2002), 237-249, with J. Adámek, H. Herrlich and W.Tholen

Injectivity and accessible categories, Cubo Matem. Educ. 4 (2002), 201-211

Modal predicates and coequations, Electronic Notes in Theor. Comp. Sci. 65, 1 (2002), with A.Kurz

Classification of accessible categories, J. Pure Appl. Alg. 175 (2002), 7-30 with J. Adámek, F. Borceux and S. Lack

Injective hulls are not natural, Alg. Univ. 48 (2002), 379-388 with J.Adámek, H.Herrlich and W.Tholen

More on injectivity in locally presentable categories, Th. Appl. Categ. 10 (2002), 148-161 with J.Adámek and F.Borceux

On the duality between varieties and algebraic theories, Alg. Univ. 49 (2003), 35-49, with J.Adámek and F.W.Lawvere

Continuous categories revisited, Th. Appl. Categ. 11 (2003), 252-282 with J.Adámek and F.W.Lawvere

Left-determined model categories and universal homotopy theories, Trans. Amer. Math. Soc. 355 (2003), 3611-3623 with W.Tholen

On pure subobjects and pure quotients, Czech. Math. Jour. 54 (2004), 623-636 with J.Adámek

On projectivity in locally presentable categories, J. Alg. 272 (2004), 701-710

Toward a characterization of algebraic exactness, J. Alg. 272 (2004), 730-738 with J.Adámek

A characterization of locally D-presentable categories, Cah. Top. Geom. Diff. Cat. XLV (2004), 141-146 with C.Centazzo and E.M.Vitale

On von Neumann varieties, Th. Appl. Cat. 13 (2004), 5-26 with F.Borceux

Semi-abelian monadic categories, Th. Appl. Cat. 13 (2004), 106-113 with M.Gran

Special reflexive graphs in modular varieties, Alg. Univ. 52 (2004), 89-102 with M.Gran

When is flatness coherent?, Comm. in Alg. 33 (2005), 1903-1912 with T.Beke and P.Karazeris

Weak factorization systems, fractions and homotopies, Appl. Cat. Struct. 13 (2005), 141-160 with A.Kurz

Pure morphisms in pro-categories, J. Pure Appl. Alg. 207 (2006), 19-35 with J.Adámek

Purity in algebra, with F.Borceux, Alg. Univ. 56 (2007), 17-35

Factorizations, fibrations and torsion, J. Homot. Relat. Struct. 2 (2007). 295-314 with W. Tholen

A convenient category for directed homotopy, with L. Fajstrup, Th. Appl. Cat. 21 (2008), 7-20

Mal'cev conditions revisited, with D. Bourn, Appl. Cat. Str. 16 (2008), 723-733

On combinatorial model categories, Appl. Cat. Str. 17 (2009), 303-316

Are all cofibrantly generated model categories combinatorial?, Cah. Top. Geom. Diff. Cat. 50 (2009), 233-238

What are sifted colimits?, Th. Appl. Cat. 23 (2010), 251-260, with J.Adámek and E. M. Vitale

Notions of Lawvere theory, Appl. Categ. Struct. 19 (2011), 363-391, with S. Lack, arXiv:0810.2578

Enriched weakness, J. Pure Appl. Alg. 216 (2012), 1807-1822, arXiv:1009.1678, with S. Lack

Abstract elementary classes and accessible categories, Annals Pure Appl. Logic 163 (2012), 2008-2017, with T. Beke

Birkhoff's variety theorem in many sorts, Alg. Univ. 68 (2012), 39-42, with J.Adámek and E. M. Vitale

Locally class-presentable and class-accessible categories, J. Pure Appl. Alg. 216 (2012), 2113-2125, with B. Chorny, arXiv:1110.0605

Class-combinatorial model categories, Homology Homotopy Appl. 14 (2012), 263-280, with B. Chorny, arXiv:1110.4252

Strongly complete logics for coalgebras, Log. Met. Comp. Sci. 8 (2012), 1-32, with A. Kurz, arXiv:1207.2732

Colimits of accessible categories, with R. Paré, Math. Proc. Cambr. Phil. Soc. 155 (2013), 47-50, arXiv:1110.0767

Are all localizing subcategories of stable homotopy categories coreflective?, with C. Casacuberta and J. J. Gutiérrez, Adv. Math. 252 (2014), 158-184, arXiv:1106.2218

On a fat small object argument, with M. Makkai and L. Vokrinek, Adv. Math. 254 (2014), 49-68, arXiv:1304.6974

A generalization of Ohkawa's theorem, with C. Casacuberta and J. J. Gutiérrez, Compositio Math. 150 (2014), 893-902, arXiv:1203.6395

Cellular categories, with M. Makkai, J. Pure Appl. Algebra 218 (2014), 1652-1664, arXiv:1304.7572

Definable orthogonality classes in accessible categories are small, J. Europ. Math. Soc. 17 (2015), arXiv:1101.2792, with J. Bagaria, C. Casacuberta and A. R. D. Matthias

Rigidification of algebras over essentially algebraic theories, Appl. Cat. Struct. 23 (2015), 159-175, arXiv:1206.0422

The accesibility rank of weak equivalences, with G. Raptis, Theory Appl. Categ. 30 (2015), 687-703, arXiv:1403.3042

On reflective subcategories of locally presentable categories, with J. Adámek, arXiv:1504.04683, Th. Appl. Cat. 30 (2015), 1306-1318.

Limits of abstract elementary classes, with M. Lieberman, arXiv:1504.04683, Th. Appl. Cat. 30 (2015), 1647-1658

Cellular objects and Shelah's singular compactness theorem, with T. Beke, arXiv:1406.3819, J. Pure Appl. Alg. 220 (2016), 1813-1836

Classification theory for accessible categories, with M. Lieberman, J. Symb. Logic, 81 (2016), 151-165, arXiv:1404.2528

Homotopy theory of enriched categories, with S. Lack, Theory Appl. Categ., 31 (2016), 712-754

$\mu$-abstract elementary classes and other generalizations, with W. Boney, R. Grossberg, M. Lieberman and S. Vasey, J. Pure Appl. Alg. 220 (2016), 3048-3066, arXiv:1509.07377

Accessible images revisited, with A. Brooke-Taylor, Proc. AMS 145 (2017), 1317-1327, arXiv:1506.01986

Accessible model categories, Appl. Cat. Str. 25 (2017), 187-196, arXiv:1503.05010

Covers, envelopes, and cotorsion theories in locally presentable abelian categories and contramodule categories, with L. Positselski, J. Alg. 483 (2017), 83-128, arXiv:1512.08119

Metric abstract elementary classes as accessible categories, with M. Lieberman, J. Symb. Logic. 82 (2017), 1022-1040, arXiv:1504.02660

Definable categories, with A. Kuber, J. Pure Appl. Algebra 222 (2018), 1006-1025, arXiv:1612.03711

Small presentations of model categories and Vopěnka's principle, with G. Raptis, Homol. Homot. Appl. 20 (2018), 303-328, arXiv:1703.08094

Algebra and local presentability: how algebraic are they?, with J. Adámek, Tbilisi Math. Jour. 10 (2017), 279-295

Nearly locally presentable categories, with L. Positselski, Th. Appl. Cat. 33 (2018), 253-264

Hanf numbers via accessible images, with M. Lieberman, Log. Meth. Comp. Sci. 13 (2017), 1-15, arXiv:1610.07816

Elementary equivalences and accessible functors, with T. Beke, Annals Pure Appl. Logic 169 (2018), 674-703, arXiv:1603.02500

Approximate injectivity, with W. Tholen,, Appl. Categ. Struct. 26 (2018), 699-716, arXiv:1608.05524

Universal abstract elementary classes and locally multipresentable categories, with M. Lieberman and S. Vasey, Proc. AMS 147 (2019), 1283-1298, arXiv:1707.09005

Internal sizes in $\mu$-abstract elementary classes, with M. Lieberman and S. Vasey, J. Pure Appl. Alg. 223 (2019), 4560-4582, arXiv:1708.06782

Forking independence from the categorical point of view, with M. Lieberman and S. Vasey, Adv. Math. 346 (2019), 719-772, arXiv:1802.09001

Factorization and local presentability in topological and uniform spaces, with M. Husek, Top. Appl. 259 (2019), 251-266.

On the unicity of cellular injectives, Math. Proc. Cambr. Phil. Soc. 167 (2019), 489-504, arXiv:1702.08684

How nice are free completions of categories, with J. Adámek, Top. Appl. 273 (2020), 106972, arXiv:1608.02524

Colimit-dense subcategories, with J. Adámek, A. Brooke-Taylor , T. Campion and L. Positselski, Comment. Math. Univ. Carol. 60 (2019), 447-462,, arXiv:1812.10649

Cofibrant generation of pure monomorphisms, with M. Lieberman, L. Positselski and S. Vasey, J. Algebra 560 (2020), 1297-1310, arXix:2001.02062.

Sizes and filtrations in accessible categories, with M. Lieberman and S. Vasey, Isr. J. Math. 238 (2020), 243-278, arXiv:1902.06777

Remarks on combinatorial and accessible model categories, Th. Appl. Categ. 37 (2021), 266-275, arXiv:2006.03251

Minimal accessible categories, Th. Appl. Categ. 36 (2021), 280-287, arXiv:2007.09967

Are chain complete posets co-wellpowered?, with J. Jurka, Order 39 (2022), 71-76, arXiv:2007.02255

Are Banach spaces monadic?, Comm. Alg. 50 (2022), 268-274, arXiv:2011.07543

Metric monads, Math. Struct. Comp. Sci. 31 (2021), 535-552, arXiv:2012.14641

Which categories are varieties?, with J. Adámek, LIPIcs Vol. 211, CALCO 2021, 6:1-6:14

Hilbert spaces and $C^\ast$-algebras are not finitely concrete, with M. Lieberman and S. Vasey, J. Pure Appl. Alg. 227 (2023), 107245, arXiv:1908.10200

Approximate injectivity and smallness in metric enriched categories, with J. Adámek, J. Pure Appl. Alg. 226 (2022), 106974, arXiv:2006.01399

Enriched locally presentable categories, with I. Di Liberti, Th. Appl. Categ., 38 (2022), 661-68, arXiv:2009.10980

Induced and higher-dimensional stable independence, with M. Lieberman and S. Vasey, Ann. Pure Appl. Logic 173 (2022), 103124, arXiv:2011.139.62

Varieties of ordered algebras as categories, with J. Adámek, Alg. Univ. 84:9 (2023), arXiv:2110.06613<\a>

Tameness in generalized metric structures, with M. Lieberman and P. Zambrano, Archive Math. Logic 62 (2023), 531-558, arXiv:1810.02317

Cellular categories and stable independence, with M. Lieberman and S. Vasey, J. Symb. Logic 88 (2023), 811-834, arXiv:1904.05691

Enriched purity and presentability in Banach spaces, Comm. Alg. 51 (2023), 5242-5262, arXiv:2206.0854

Smallness in topology, with J. Adámek, M. Husek and W. Tholen, Quest. Math. 46 (2023), 13-39, arXiv:2302.0050

Discrete equational theories, Math. Struct. Comp. Sci. 34 (2024), 147-160, arXiv:2204.02590

To appear shortly

Fibrantly generated weak factorization systems, with S. Cox, arXiv:2201.06782, to appear in Rend. Mat. Univ. Padova

Papers submitted for publication

Notions of enriched purity, with G. Tendas, arXiv:2303.11957

Relative injective modules, superstability and noetherian categories, with M. Mazari-Armida, arXiv:2308.02456

Enriched universal algebra, with G. Tendas, arXiv:2310.11972<\a>

Unstable independence from the categorical point of view, with M.Kamsma, arXiv:2310.15804

Others

Generalized Brown representability in homotopy categories, corrected version of Theory Appl. Categ. 14 (2005), 451-479

On homotopy varieties, corrected version of Adv. Math. 214 (2007), 525-550

Talks

Class-combinatorial model categories, Calais 2008

Homotopy accessible categories, Brussels 2008

Phantom accessible triangulated categories, Paderborn 2009

Facets of accessibility, Durham 2009

Generalized purity, definability and Brown representability, Praha 2009

Enriched weakness, Genova 2010

Accessible categories and inaccessible cardinals, Barcelona 2011

Combinatorial categories, Coimbra 2012

Good colimits, weak factorization systems and model categories, Murcia 2013

Towards categorical model theory, Cambridge 2014

Towards categorical model theory, Stockholm 2014

Classification theory for accessible categories, Aveiro 2015

Inaccessible cardinals and accessible categories, Cambridge 2015

Homotopy locally presentable enriched categories, Bonn 2016

Forking in accessible categories, Leeds 2018

Přednášky

Matematická logika

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Teorie množin

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Diskrétní matematika

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Algebra 3

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