Embedding of Accessible Regular Categories

1989 ◽  
Vol 32 (2) ◽  
pp. 241-247
Author(s):  
Michael Barr
Keyword(s):  
Regular Embedding ◽  
Functor Category ◽  
Accessible Category

AbstractThe purpose of this note is to prove that a regular accessible category has a full regular embedding into a set-valued functor category.

scholarly journals Generic immersions and totally real embeddings

2018 ◽  
Vol 29 (11) ◽  
pp. 1850073 ◽  
Author(s):  
Naohiko Kasuya ◽  
Masamichi Takase
Keyword(s):  
Regular Embedding ◽  
Simply Connected ◽  
Totally Real

We show that, for a closed orientable [Formula: see text]-manifold, with [Formula: see text] not congruent to 3 modulo 4, the existence of a CR-regular embedding into complex [Formula: see text]-space ensures the existence of a totally real embedding into complex [Formula: see text]-space. This implies that a closed orientable [Formula: see text]-manifold with non-vanishing Kervaire semi-characteristic possesses no CR-regular embedding into complex [Formula: see text]-space. We also pay special attention to the cases of CR-regular embeddings of spheres and of simply-connected 5-manifolds.

On the extension of real regular embedding

2008 ◽  
Vol 40 (5) ◽  
pp. 801-806 ◽  
Author(s):  
Zbigniew Jelonek
Keyword(s):  
Regular Embedding

A computationally adequate model for overloading via domain-valued functors

1998 ◽  
Vol 8 (4) ◽  
pp. 321-349 ◽  
Author(s):  
HIDEKI TSUIKI
Keyword(s):  
Infinite Number ◽  
Denotational Semantics ◽  
Single Equation ◽  
Minimal Solution ◽  
Adequate Model ◽  
Functor Category ◽  
Syntactic Properties ◽  
Recursive Equations

We give a denotational semantics to a calculus λ[otimes ] with overloading and subtyping. In λ[otimes ], the interaction between overloading and subtyping causes self application, and non-normalizing terms exist for each type. Moreover, the semantics of a type depends not on that type alone, but also on infinitely many others. Thus, we need to consider infinitely many domains, which are related by an infinite number of mutually recursive equations. We solve this by considering a functor category from the poset of types modulo equivalence to a category in which each type is interpreted. We introduce a categorical constructor corresponding to overloading, and formalize the equations as a single equation in the functor category. A semantics of λ[otimes ] is then expressed in terms of the minimal solution of this equation. We prove the adequacy theorem for λ[otimes ] following the construction in Pitts (1994) and use it to derive some syntactic properties.

scholarly journals Exponential Objects

2015 ◽  
Vol 23 (4) ◽  
pp. 351-369
Author(s):  
Marco Riccardi
Keyword(s):  
Natural Transformation ◽  
Universal Property ◽  
Free Object ◽  
Standard Definition ◽  
Object Category ◽  
Functor Category ◽  
Exponential Object ◽  
Definition Of ◽  
Initial Object

Summary In the first part of this article we formalize the concepts of terminal and initial object, categorical product [4] and natural transformation within a free-object category [1]. In particular, we show that this definition of natural transformation is equivalent to the standard definition [13]. Then we introduce the exponential object using its universal property and we show the isomorphism between the exponential object of categories and the functor category [12].

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