Are Operads Algebraic Theories
نویسنده
چکیده
I exhibit a pair of non-symmetric operads that, while not themselves isomorphic, induce isomorphic monads. The existence of such a pair implies that if ‘algebraic theory’ is understood as meaning ‘monad’ then operads cannot be regarded as algebraic theories of a special kind.
منابع مشابه
Elements of a theory of algebraic theories
Kleisli bicategories are a natural environment in which the combinatorics involved in various notions of algebraic theory can be handled in a uniform way. The setting allows a clear account of comparisons between such notions. Algebraic theories, symmetric operads and nonsymmetric operads are treated as examples.
متن کامل$omega$-Operads of coendomorphisms and fractal $omega$-operads for higher structures
In this article we introduce the notion of textit{Fractal $omega$-operad} emerging from a natural $omega$-operad associated to any coglobular object in the category of higher operads in Batanin's sense, which in fact is a coendomorphism $omega$-operads. We have in mind coglobular object of higher operads which algebras are kind of higher transformations. It follows that this natural $omeg...
متن کاملOperads from the viewpoint of categorical algebra
We exhibit a parallel between Lawvere’s algebraic theories and operads; there is a common ancestor of both notions whose syntax is described by labeled trees, dummy variables corresponding to special labels. Operads, cyclic and braided operads alike arise as group objects in the category of compositional structures. Laplaza’s coherence theorem for “associativity not an isomorphism” is seen to c...
متن کاملOperads and Conformal Field Theory Lecture 1: Conformal Field Theory
Physicists have developed very advanced methods to compute such integrals. For example, the famous Feynman diagram technique allows us to compute the above integral for a rather particular function S(x), a small perturbation of a positive de nite quadratic form in R . Sometimes, elaborate techniques of physicists to compute simple things nd an amazing application to very general things in mathe...
متن کاملOperads in algebraic combinatorics
The main ideas developed in this habilitation thesis consist in endowing combinatorial objects (words, permutations, trees, Young tableaux, etc.) with operations in order to construct algebraic structures. This process allows, by studying algebraically the structures thus obtained (changes of bases, generating sets, presentations, morphisms, representations), to collect combinatorial informatio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006