On Iteratable Endofunctors
نویسنده
چکیده
Completely iterative monads of Elgot et al. are the monads such that every guarded iterative equation has a unique solution. Free completely iterative monads are known to exist on every iteratable endofunctor H, i. e., one with final coalgebras of all functors H( ) + X. We show that conversely, if H generates a free completely iterative monad, then it is iteratable.
منابع مشابه
Adjunctions between Hom and Tensor as endofunctors of (bi-) module category of comodule algebras over a quasi-Hopf algebra.
For a Hopf algebra H over a commutative ring k and a left H-module V, the tensor endofunctors V k - and - kV are left adjoint to some kinds of Hom-endofunctors of _HM. The units and counits of these adjunctions are formally trivial as in the classical case.The category of (bi-) modules over a quasi-Hopf algebra is monoidal and some generalized versions of Hom-tensor relations have been st...
متن کاملFunctorial Factorization, Well-pointedness and Separability
A functorial treatment of factorization structures is presented, under extensive use of well-pointed endofunctors. Actually, so-called weak factorization systems are interpreted as pointed lax indexed endofunctors, and this sheds new light on the correspondence between reeective subcategories and factorization systems. The second part of the paper presents two important factorization structures...
متن کاملCoherence for monoidal endofunctors
The goal of this paper is to prove coherence results with respect to relational graphs for monoidal endofunctors, i.e. endofunctors of a monoidal category that preserve the monoidal structure up to a natural transformation that need not be an isomorphism. These results are proved first in the absence of symmetry in the monoidal structure, and then with this symmetry. In the later parts of the p...
متن کاملPolynomial Functors and Trees
We explore the relationship between polynomial functors and trees. In the first part we characterise trees as certain polynomial functors and obtain a completely formal but at the same time conceptual and explicit construction of two categories of rooted trees, whose main properties we describe in terms of some factorisation systems. The second category is the category Ω of Moerdijk and Weiss. ...
متن کاملTensoring with Infinite-dimensional Modules in O 0 Tensoring with Infinite-dimensional Modules in O 0
We show that the principal block O0 of the BGG category O for a semisimple Lie algebra g acts faithfully on itself via exact endofunctors which preserve tilting modules, via right exact endofunctors which preserve projective modules and via left exact endofunctors which preserve injective modules. The origin of all these functors is tensoring with arbitrary (not necessarily finite-dimensional) ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electr. Notes Theor. Comput. Sci.
دوره 69 شماره
صفحات -
تاریخ انتشار 2002