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Latent fibrations are an adaptation, appropriate for categories of partial maps (as presented by restriction categories), of the usual notion of fibration. This paper initiates the development of the basic theory of latent fibrations and explores some key examples. Latent fibrations cover a wide variety of examples, some of which are partial versions of standard fibrations, and some of which are particular to partial map categories (particularly those that arise in computational settings). Latent fibrations with various special properties are identified: hyperconnected latent fibrations, in particular, are shown to support the construction of a fibrational dual - important to reverse differential programming and, more generally, in the theory of lenses.
@article{TAC_2021_36_a15,
author = {Robin Cockett and Geoff Cruttwell and Jonathan Gallagher and Dorette Pronk},
title = {Latent {Fibrations:} {Fibrations} for {Categories} of {Partial} {Maps}},
journal = {Theory and applications of categories},
pages = {423--491},
publisher = {mathdoc},
volume = {36},
year = {2021},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TAC_2021_36_a15/}
}
TY - JOUR AU - Robin Cockett AU - Geoff Cruttwell AU - Jonathan Gallagher AU - Dorette Pronk TI - Latent Fibrations: Fibrations for Categories of Partial Maps JO - Theory and applications of categories PY - 2021 SP - 423 EP - 491 VL - 36 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TAC_2021_36_a15/ LA - en ID - TAC_2021_36_a15 ER -
%0 Journal Article %A Robin Cockett %A Geoff Cruttwell %A Jonathan Gallagher %A Dorette Pronk %T Latent Fibrations: Fibrations for Categories of Partial Maps %J Theory and applications of categories %D 2021 %P 423-491 %V 36 %I mathdoc %U http://geodesic.mathdoc.fr/item/TAC_2021_36_a15/ %G en %F TAC_2021_36_a15
Robin Cockett; Geoff Cruttwell; Jonathan Gallagher; Dorette Pronk. Latent Fibrations: Fibrations for Categories of Partial Maps. Theory and applications of categories, The Rosebrugh Festschrift, Tome 36 (2021), pp. 423-491. http://geodesic.mathdoc.fr/item/TAC_2021_36_a15/