Matías Menni's research

Research papers (in reverse chronological order)

1. The étendue of a combinatorial space and its dimension. Advances in Mathematics 459 (2024).

2. The least subtopos containing the discrete skeleton of Ω. Theory Appl. Categ. 42 (2024), 172-179.

3. Decidable objects and molecular toposes. Rev. Un. Mat. Argentina 67, no. 2 (2024), 397–415.

4. Positive rigs. Forum Mathematicum 36, no. 4 (2024), 897-913.

5. Bi-directional models of 'radically synthetic' differential geometry. Theory Appl. Categ. 40 (2024), 413–429.

6. (With V. Marra) Separable MV-algebras and lattice-groups. Journal of Algebra 646, (2024), 66-99.

7. The successive dimension, without elegance. Proc. of the American Mathematical Society 152, No. 3 (2024), 1337-1354.

8. Maps with Discrete Fibers and the Origin of Basepoints. Appl. Categor. Struct. 30, (2022), 991–1015.

9. A Basis Theorem for 2-rigs and Rig Geometry. Cah. Topologie Géom. Différ. Catégoriques 62, No. 4 (2021), 451-490.

10. (With F. Marmolejo) The canonical intensive quality of a cohesive topos. Theory Appl. Categ. 36 (2021), 250-279.

11. The hyperconnected maps that are local. J. Pure Appl. Algebra 225, No. 5, Article ID 106596, 15 p. (2021).

12. (With F. Marmolejo) Level ε. Cah. Topologie Géom. Différ. Catégoriques 60, No. 4 (2019), 450-477.

13. Monic skeleta, Boundaries, Aufhebung, and the meaning of 'one-dimensionality'. Theory Appl. Categ. 34 (2019), 714-735.

14. Every Sufficiently Cohesive topos is infinitesimally generated. Cah. Topologie Géom. Différ. Catégoriques 60, No. 1 (2019), 3-31.

15. The Unity and Identity of decidable objects and double-negation sheaves. Journal of Symbolic Logic 83, no. 4 (2018), 1667-1679.

16. The construction of \pi_0 in Axiomatic Cohesion. Tbilisi Mathematical Journal 10(3)  (2017), 183–207.

17. Every rig with a one-variable fixed point presentation is the Burnside rig of a prextensive category. Applied Categorical Structures 25 (2017), 663-707.

18. (With F. Marmolejo) On the relation between continuous and combinatorial. Journal of Homotopy and Related Structures 12 (2017), 379-412.

19. (With J. L. Castiglioni and W. J. Zuluaga Botero) A representation theorem for integral rigs and its applications to residuated lattices. J. Pure Appl. Algebra 220, no. 10 (2016), 3533-3566.

20. (With F. W. Lawvere) Internal choice holds in the discrete part of any cohesive topos satisfying stable connected codiscreteness. Theory Appl. Categ. 30 (2015), 909-932.

21. Continuous Cohesion over sets. Theory Appl. Categ. 29 (2014), 542-568.

22. Sufficient Cohesion over atomic toposes. Cah. Topologie Géom. Différ. Catégoriques 55, No. 2 (2014), 113-149.

23. (With C. Smith) Modes of adjointness. Journal of Philosophical Logic 43 (2014), 365-391.

24. Bimonadicity and the explicit basis property. Theory Appl. Categ. 26 (2012), 554–581.

25. (With F. W. Lawvere) The Hopf algebra of Möbius intervals. Theory Appl. Categ. 24 (2010), 221–265.

26. Läuchli's completeness theorem from a topos-theoretic perspective. Appl. Categ. Structures 18 (2010), 185–197.

27. Algebraic categories whose projectives are explicitly free. Theory Appl. Categ. 22 (2009), 509–541.

28. (With J. L. Castiglioni and M. Sagastume) Compatible operations on commutative residuated lattices. J. Appl. Non-Classical Logics 18 (2008), 413–425.

29. (With J. L. Castiglioni and M. Sagastume) On some categories of involutive centered residuated lattices. Studia Logica 90 (2008), 93–124.

30. Combinatorial functional and differential equations applied to differential posets. Discrete Math. 308 (2008), 1864–1888.

31. (With N. Sabadini and R. F. C. Walters) A universal property of the monoidal 2-category of cospans of ordinals and surjections. Theory Appl. Categ. 18 (2007), 631–653.

32. Cocomplete toposes whose exact completions are toposes. J. Pure Appl. Algebra 210 (2007), 511–520.

33. (With M. Fiore) Reflective Kleisli subcategories of the category of Eilenberg-Moore algebras for factorization monads. Theory Appl. Categ. 15 (2005/06), 40–65.

34. Symmetric monoidal completions and the exponential principle among labeled combinatorial structures. Theory Appl. Categ. 11 (2003), 397–419.

35. About И-quantifiers. Appl. Categ. Structures 11 (2003), 421–445.

36. A characterization of the left exact categories whose exact completions are toposes. J. Pure Appl. Algebra 177 (2003), 287–301.

37. (With A. Simpson) Topological and limit-space subcategories of countably-based equilogical spaces. Math. Structures Comput. Sci. 12 (2002), 739–770.

38. More exact completions that are toposes. Ann. Pure Appl. Logic 116 (2002), 187–203.

39. Closure operators in exact completions. Theory Appl. Categ. 8 (2001), 522–540.

PhD thesis

Exact completions and toposes.