Algebraic theories : a categorical introduction to general algebra [E-Book] / J. Adámek, J. Rosický, E.M. Vitale ; with a foreword by F .W. Lawvere.
Adámek, Jiří, (author)
Rosický, Jiří, (author) / Vitale, E. M., (author) / Lawvere, F .W., (writer of foreword)
Cambridge : Cambridge University Press, 2011
1 online resource (xvii, 249 pages)
Cambridge tracts in mathematics ; 184
Full Text
Table of Contents:
  • Foreword / F.W. Lawvere
  • Preliminaries. Abstract Algebraic Categories. Algebraic theories and algebraic categories ; Sifted and filtered colimits ; Reflexive coequalizers ; Algebraic categories as free completions ; Properties of algebras ; A characterization of algebraic categories ; From filtered to sifted ; Canonical theories ; Algebraic functors ; Birkhoff's variety theorem
  • Concrete algebraic categories. One-sorted algebraic categories ; Algebras for an endofunctor ; Equational categories of [SIGMA]-algebras ; S-sorted algebraic categories
  • Selected topics. Morita equivalence ; Free exact categories ; Exact completion and reflexive-coequalizer completion ; Finitary localizations of algebraic categories. Monads ; Abelian categories ; More about dualities for one-sorted algebraic categories.