Watanabe H., A criterion for the existence of subobject classifiers, Hokkaido Mathematical Journal(to appear), 1998.  Home/Search Document Details and Download
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The Subobject Classifier of the Category of Functional.. - Watanabe (1998) (1 citation) Self-citation (Watanabe) (Correct)
....proved by using the theory of hypersets. In this paper, we prove the existence of subobject classifier in NDyn by using the construction via presheaves over Tree in the same way as the proof of monoidal closedness in [8] The proof uses a general lemma about presheaf categories, which is given in [10]. As we remark later, NDyn is a category of coalgebras for finite powerset functor without empty set. We can brush up the technique which is used in this paper, to an existence theorem[7] of subobject classifiers in categories of coalgebras by using accessible category theory, which led to another ....
....cocompleteness. We give the concrete construction of coproduct and coequalizer. In Section 3, we show the existence of small, dense subcategory Tree in NDyn. Then the category NDyn turns out to be a reflective subcategory of Set Tree op , and hence complete. We apply the criterion given in [10], and show the existence of subobject classifier in Section 4. 2 The category NDyn 2.1 Definitions First of all, we recall the definitions of nondeterministic dynamical systems and the category NDyn they form. Definition 2.1. A nondeterministic dynamical system D = jDj; D ) consists of a set ....
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Watanabe H., A criterion for the existence of subobject classifiers, Hokkaido Mathematical Journal(to appear), 1998.
An Axiomatics for Categories of Coalgebras - Power, Watanabe (1998) (4 citations) Self-citation (Watanabe) (Correct)
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H. Watanabe, A criterion for the existence of subobject classifiers (submitted).
An Axiomatics for Categories of Transition Systems as.. - Johnstone, Power.. (1998) (2 citations) (Correct)
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H. Watanabe, A criterion for the existence of subobject classifiers (draft).
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