# Matías Menni's research

## Research papers (in reverse chronological order)

- The Unity and Identity of decidable objects and double-negation sheaves. To appear in the Journal of Symbolic Logic.
- Every Sufficiently Cohesive topos is infinitesimally generated. To appear in the CTGDC.
- The construction of \pi_0 in Axiomatic Cohesion. Tbilisi Mathematical Journal 10(3) (2017), 183–207.
- Every rig with a one-variable fixed point presentation is the Burnside rig of a prextensive category.
*Applied Categorical Structures*25 (2017), 663-707. - (With F. Marmolejo) On the relation between continuous and combinatorial.
*Journal of Homotopy and Related Structures*12 (2017), 379-412. - (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 (2016), no. 10, 3533-3566. - (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. - Continuous Cohesion over sets.
*Theory Appl. Categ.*29 (2014), 542-568. - Sufficient Cohesion over atomic toposes.
*Cah. Topologie Géom. Différ. Catégoriques*55, No. 2 (2014), 113-149. - (With C. Smith) Modes of adjointness.
*Journal of Philosophical Logic*43 (2014), 365-391. - Bimonadicity and the explicit basis property.
*Theory Appl. Categ.*26 (2012), 554–581. - (With F. W. Lawvere) The Hopf algebra of Möbius intervals.
*Theory Appl. Categ.*24 (2010), 221–265. - Läuchli's completeness theorem from a topos-theoretic perspective.
*Appl. Categ. Structures*18 (2010), 185–197. - Algebraic categories whose projectives are explicitly free.
*Theory Appl. Categ.*22 (2009), 509–541. - (With J. L. Castiglioni and M. Sagastume) Compatible operations on commutative residuated lattices.
*J. Appl. Non-Classical Logics*18 (2008), 413–425. - (With J. L. Castiglioni and M. Sagastume) On some categories of involutive centered residuated lattices.
*Studia Logica*90 (2008), 93–124. - Combinatorial functional and differential equations applied to differential posets.
*Discrete Math.*308 (2008), 1864–1888. - (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. - Cocomplete toposes whose exact completions are toposes.
*J. Pure Appl. Algebra*210 (2007), 511–520. - (With M. Fiore) Reflective Kleisli subcategories of the category of Eilenberg-Moore algebras for factorization monads.
*Theory Appl. Categ.*15 (2005/06), 40–65. - Symmetric monoidal completions and the exponential principle among labeled combinatorial structures.
*Theory Appl. Categ.*11 (2003), 397–419. - About И-quantifiers.
*Appl. Categ. Structures*11 (2003), 421–445. - A characterization of the left exact categories whose exact completions are toposes.
*J. Pure Appl. Algebra*177 (2003), 287–301. - (With A. Simpson) Topological and limit-space subcategories of countably-based equilogical spaces.
*Math. Structures Comput. Sci.*12 (2002), 739–770. - More exact completions that are toposes.
*Ann. Pure Appl. Logic*116 (2002), 187–203. - Closure operators in exact completions.
*Theory Appl. Categ.*8 (2001), 522–540.