The logic of structures

Ageron, Pierre

doi:10.1016/0022-4049(92)90123-w

Cited by 3 publications

(3 citation statements)

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“…We now obtain the following characterization theorem for n-accessible categories with wide pullbacks (see also Theorem 0.20 of [23] and Theorem 4.11 of [3]):…”

Section: 3mentioning

confidence: 99%

“…[11,19,15,8,18]) -wide pullbacks = locally polypresentable categories (cf. [23,31,3,16]; see also [12] for background).…”

Section: Introductionmentioning

confidence: 99%

“…The answer is given in Section 1 of this paper: colimits of some diagrams C: G --~ Set, with a small groupoid G; here G may be assumed to be skeletal, so that it is just a disjoint union of groups Gi, and "some" means that each group action given by C must be free. We call such colimits quasi-coproducts; they appear less explicity in conjunction with "Galois sketches" in [3] and with "pullback theories" in [16].…”

Section: Introductionmentioning

confidence: 99%

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Quasi-coproducts and accessible categories with wide pullbacks

Tholen

1996

Appl Categor Struct

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We establish a 2-categorical duality involving the 2-category .A,~ of all to-accessible categories with wide pullbacks, also known as locally tc-polypresentable categories, and of functors preserving ~¢-filtered colimits and wide puUbacks. Commutation of wide pullbacks with so-called quasi-coproducts in Set is the basic ingredient to this duality, which leads to a full characterization of categories of type Wdpb Filt,~(A, Set) = .A,~ (1991). 18A35, 18B40, 18C99. Mathematics Subject Classifications

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“…We now obtain the following characterization theorem for n-accessible categories with wide pullbacks (see also Theorem 0.20 of [23] and Theorem 4.11 of [3]):…”

Section: 3mentioning

confidence: 99%

“…[11,19,15,8,18]) -wide pullbacks = locally polypresentable categories (cf. [23,31,3,16]; see also [12] for background).…”

Section: Introductionmentioning

confidence: 99%