Elementary fibrations of enriched groupoids
The present paper aims at stressing the importance of the Hofmann–Streicher groupoid model for Martin Löf Type Theory as a link with the first-order equality and its semantics via adjunctions. The groupoid model was introduced by Martin Hofmann in his Ph.D. thesis and later analysed in collaboration...
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| Veröffentlicht in: | Mathematical structures in computer science 2021-10, Vol.31 (9), p.958-978 |
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| container_title | Mathematical structures in computer science |
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| creator | Emmenegger, Jacopo Pasquali, Fabio Rosolini, Giuseppe |
| description | The present paper aims at stressing the importance of the Hofmann–Streicher groupoid model for Martin Löf Type Theory as a link with the first-order equality and its semantics via adjunctions. The groupoid model was introduced by Martin Hofmann in his Ph.D. thesis and later analysed in collaboration with Thomas Streicher. In this paper, after describing an algebraic weak factorisation system
$$\mathsf {L, R}$$
on the category
$${\cal C}-{\cal Gpd}$$
of
$${\cal C}$$
-enriched groupoids, we prove that its fibration of algebras is elementary (in the sense of Lawvere) and use this fact to produce the factorisation of diagonals for
$$\mathsf {L, R}$$
needed to interpret identity types. |
| doi_str_mv | 10.1017/S096012952100030X |
| format | Article |
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$$\mathsf {L, R}$$
on the category
$${\cal C}-{\cal Gpd}$$
of
$${\cal C}$$
-enriched groupoids, we prove that its fibration of algebras is elementary (in the sense of Lawvere) and use this fact to produce the factorisation of diagonals for
$$\mathsf {L, R}$$
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$$\mathsf {L, R}$$
on the category
$${\cal C}-{\cal Gpd}$$
of
$${\cal C}$$
-enriched groupoids, we prove that its fibration of algebras is elementary (in the sense of Lawvere) and use this fact to produce the factorisation of diagonals for
$$\mathsf {L, R}$$
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$$\mathsf {L, R}$$
on the category
$${\cal C}-{\cal Gpd}$$
of
$${\cal C}$$
-enriched groupoids, we prove that its fibration of algebras is elementary (in the sense of Lawvere) and use this fact to produce the factorisation of diagonals for
$$\mathsf {L, R}$$
needed to interpret identity types.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/S096012952100030X</doi><tpages>21</tpages><orcidid>https://orcid.org/0000-0003-1672-9368</orcidid><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
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| ispartof | Mathematical structures in computer science, 2021-10, Vol.31 (9), p.958-978 |
| issn | 0960-1295 1469-8072 |
| language | eng |
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| source | Cambridge Journals |
| subjects | Algebra Collaboration Computer science Equality Factorization Semantics |
| title | Elementary fibrations of enriched groupoids |
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