Bilinearity and Cartesian Closed Monads.
نویسندگان
چکیده
منابع مشابه
Cartesian closed subcategories of topological fuzzes
A category $mathbf{C}$ is called Cartesian closed provided that it has finite products and for each$mathbf{C}$-object $A$ the functor $(Atimes -): Ara A$ has a right adjoint. It is well known that the category $mathbf{TopFuzz}$ of all topological fuzzes is both complete and cocomplete, but it is not Cartesian closed. In this paper, we introduce some Cartesian closed subcategories of this cat...
متن کاملDependent Cartesian Closed Categories
We present a generalization of cartesian closed categories (CCCs) for dependent types, called dependent cartesian closed categories (DCCCs), which also provides a reformulation of categories with families (CwFs), an abstract semantics for Martin-Löf type theory (MLTT) which is very close to the syntax. Thus, DCCCs accomplish mathematical elegance as well as a direct interpretation of the syntax...
متن کاملCartesian closed Dialectica categories
When Gödel developed his functional interpretation, also known as the Dialectica interpretation, his aim was to prove (relative) consistency of first order arithmetic by reducing it to a quantifier-free theory with finite types. Like other functional interpretations (e.g. Kleene’s realizability interpretation and Kreisel’s modified realizability) Gödel’s Dialectica interpretation gives rise to ...
متن کاملClosed Categories Generated by Commutative Monads
The notion of commutative monad was denned by the author in [4]. The content of the present paper may briefly be stated: The category of algebras for a commutative monad can in a canonical way be made into a closed category, the two adjoint functors connecting the category of algebras with the base category are in a canonical way closed functors, and the frontand end-adjunctions are closed tran...
متن کاملMonads on Symmetric Monoidal Closed Categories By
Introduction. This note is concerned with "categories with internal horn and | and we shall use the terminology from the paper [2] by EIL~.NBERG and Kv.Imy. The result proved may be stated briefly as follows : a Y/--monad ("strong monad") on a symmetric monoidal closed category ~ carries two canonical structures as closed functor. I f these agree (in which case we call the monad commutative), t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 1971
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-11042