Kan extensions in effective semantics

1988 ◽  
pp. 121-132
Author(s):  
Philip S. Mulry
Keyword(s):  
Kan Extensions

scholarly journals Kan extensions of homotopy functors

1978 ◽  
Vol 12 (3) ◽  
pp. 253-269 ◽  
Author(s):  
Allan Calder ◽  
Jerrold Siegel
Keyword(s):  
Kan Extensions ◽  
Homotopy Functors

scholarly journals A note on čech and kan extensions of homotopy functors

1982 ◽  
Vol 25 (3) ◽  
pp. 249-250
Author(s):  
Allan Calder ◽  
Jerrold Siegel
Keyword(s):  
Kan Extensions ◽  
Homotopy Functors

Kan extensions

1986 ◽  
pp. 93-105
Author(s):  
Sten Kaijser ◽  
Joan Wick Pelletier
Keyword(s):  
Kan Extensions

scholarly journals Presheaf Models for Concurrency

1996 ◽  
Vol 3 (35) ◽  
Author(s):  
Gian Luca Cattani ◽  
Glynn Winskel
Keyword(s):  
Broad Class ◽  
General Nature ◽  
General Process ◽  
Process Calculi ◽  
Event Structures ◽  
Wide Range ◽  
Concurrent Computation ◽  
Kan Extensions ◽  
Modelling Process ◽  
Open Maps

This paper studies presheaf models for concurrent computation. An aim is to harness the general machinery around presheaves for the purposes of process calculi. Traditional models like synchronisation trees and event structures have been shown to embed fully and faithfully in particular<br />presheaf models in such a way that bisimulation, expressed through the presence of a span of open maps, is conserved. As is shown in the work of Joyal and Moerdijk, presheaves are rich in constructions which preserve open<br />maps, and so bisimulation, by arguments of a very general nature. This paper contributes similar results but biased towards questions of bisimulation in process calculi. It is concerned with modelling process constructions on presheaves, showing these preserve open maps, and with transferring such<br />results to traditional models for processes. One new result here is that a wide range of left Kan extensions, between categories of presheaves, preserve open maps. As a corollary, this also implies that any colimit-preserving functor between presheaf categories preserves open maps. A particular left Kan extension is shown to coincide with a refinement operation on event structures. A broad class of presheaf models is proposed for a general process calculus. General arguments are given for why the operations of a presheaf model preserve open maps and why for specic presheaf models the operations coincide with those of traditional models.

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