On The Axioms Of $\mathcal{M},\mathcal{N}$-Adhesive Categories
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912268846891008 |
|---|---|
| author | Castelnovo, Davide Miculan, Marino |
| author_facet | Castelnovo, Davide Miculan, Marino |
| contents | Adhesive and quasiadhesive categories provide a general framework for the study of algebraic graph rewriting systems. In a quasiadhesive category any two regular subobjects have a join which is again a regular subobject. Vice versa, if regular monos are adhesive, then the existence of a regular join for any pair of regular subobjects entails quasiadhesivity. It is also known (quasi)adhesive categories can be embedded in a Grothendieck topos via a functor preserving pullbacks and pushouts along (regular) monomorphisms. In this paper we extend these results to $\mathcal{M}, \mathcal{N}$-adhesive categories, a concept recently introduced to generalize the notion of (quasi)adhesivity. We introduce the notion of $\mathcal{N}$-adhesive morphism, which allows us to express $\mathcal{M}, \mathcal{N}$-adhesivity as a condition on the subobjects' posets. Moreover, $\mathcal{N}$-adhesive morphisms allows us to show how an $\mathcal{M},\mathcal{N}$-adhesive category can be embedded into a Grothendieck topos, preserving pullbacks and $\mathcal{M}, \mathcal{N}$-pushouts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12638 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On The Axioms Of $\mathcal{M},\mathcal{N}$-Adhesive Categories Castelnovo, Davide Miculan, Marino Logic in Computer Science Category Theory Adhesive and quasiadhesive categories provide a general framework for the study of algebraic graph rewriting systems. In a quasiadhesive category any two regular subobjects have a join which is again a regular subobject. Vice versa, if regular monos are adhesive, then the existence of a regular join for any pair of regular subobjects entails quasiadhesivity. It is also known (quasi)adhesive categories can be embedded in a Grothendieck topos via a functor preserving pullbacks and pushouts along (regular) monomorphisms. In this paper we extend these results to $\mathcal{M}, \mathcal{N}$-adhesive categories, a concept recently introduced to generalize the notion of (quasi)adhesivity. We introduce the notion of $\mathcal{N}$-adhesive morphism, which allows us to express $\mathcal{M}, \mathcal{N}$-adhesivity as a condition on the subobjects' posets. Moreover, $\mathcal{N}$-adhesive morphisms allows us to show how an $\mathcal{M},\mathcal{N}$-adhesive category can be embedded into a Grothendieck topos, preserving pullbacks and $\mathcal{M}, \mathcal{N}$-pushouts. |
| title | On The Axioms Of $\mathcal{M},\mathcal{N}$-Adhesive Categories |
| topic | Logic in Computer Science Category Theory |
| url | https://arxiv.org/abs/2401.12638 |