caa a22 4500 445378751 CHVBK 20180317143011.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s10485-009-9215-2 doi (NATIONALLICENCE)springer-10.1007/s10485-009-9215-2 Notions of Lawvere Theory [Elektronische Daten] [Stephen Lack, Jiří Rosický] Categorical universal algebra can be developed either using Lawvere theories (single-sorted finite product theories) or using monads, and the category of Lawvere theories is equivalent to the category of finitary monads on Set. We show how this equivalence, and the basic results of universal algebra, can be generalized in three ways: replacing Set by another category, working in an enriched setting, and by working with another class of limits than finite products. Springer Science+Business Media B.V., 2009 Monad nationallicence Lawvere theory nationallicence Enriched category nationallicence Locally presentable category nationallicence Sifted colimit nationallicence Lack Stephen School of Computing and Mathematics, University of Western Sydney, Locked Bag 1797, 1797, Penrith, South DC New South Wales, Australia aut Rosický Jiří Department of Mathematics and Statistics, Masaryk University, Kotlářská 2, 60000, Brno, Czech Republic aut Applied Categorical Structures Springer Netherlands 19/1(2011-02-01), 363-391 0927-2852 19:1<363 2011 19 10485 https://doi.org/10.1007/s10485-009-9215-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10485-009-9215-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lack Stephen School of Computing and Mathematics, University of Western Sydney, Locked Bag 1797, 1797, Penrith, South DC New South Wales, Australia aut NATIONALLICENCE 700 1- Rosický Jiří Department of Mathematics and Statistics, Masaryk University, Kotlářská 2, 60000, Brno, Czech Republic aut NATIONALLICENCE 773 0- Applied Categorical Structures Springer Netherlands 19/1(2011-02-01), 363-391 0927-2852 19:1<363 2011 19 10485 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer