Viktor Winschel
Dr. Viktor Winschel — monetary theory, compositional game theory, computational economics.
Full bibliographic data: References.
Monographs (with Renée Menéndez)
- MoMaT-A — axiomatic money and macro accounting: AccCat / DecCat / GovCat, gauge invariance, central bank. Authoritative German monograph of the program.
- MoMaT-I — topos of economic policy and Ouroboros deployment ladder; dual realisation of MoMaT-A on OiC.OS.
Co-authored publications
One MoMaT paper in three outlets — same core text, minimal venue-specific changes (categorical macro accounting, one-bank and three-bank models, DEB/QEB):
- MW-2025-Cat — arXiv preprint
- MW-2025-SCF — SSRN (supply-chain finance framing)
- MW-2026-Crypto — Cryptoeconomic Theory, World Scientific
Refereed journals and books
- VW-2019-UQ — global sensitivity and UQ for economic models; feeds the Sim ⊣ Est learning loop in DecCat (which parameters matter for macro accounting forecasts).
- VW-2018-CGT — open games as compositional decisions; direct precursor of DecCat and the engine’s Open Game canvas.
- VW-2017-HODT — higher-order beliefs and selection; extends compositional game theory toward institutional learning.
- VW-2016-SEHOG — equilibrium selection in higher-order games; relevant for multiple consistent macro paths under the same books.
- VW-2015-Coalg — coalgebraic infinite games; underpins non-discounted, book-consistent strategic dynamics.
- VW-2010-Econ — sparse-grid estimation without curse of dimensionality; operational backbone of MoMaT’s internal econometricians (Smolyak / JBendge line).
- VW-2008-SG — likelihood on sparse grids with Heiss; numerical core reused in MoMaT estimation pipelines.
- VW-2005-PhD — exchange-rate regimes and nonlinear econometrics; early macro–micro bridge before categorical MoMaT.
- VW-2001-Def — fiscal deficits and market discipline; fiscal–monetary link in stock-flow consistent thinking.
Working papers and preprints
- VW-2018-APA — predicting agents as algebra; anticipatory structure aligned with MoMaT’s forward/backward open-game ports.
- VW-2017-CCSG — compositional coalgebraic games; semantic layer behind DecCat morphisms.
- VW-2016-CSDGT — string diagrams for game theory; visual language now used in the engine UI.
- VW-2009-JBendge — object-oriented DSGE solve/estimate/select; prototype of MoMaT’s embedded Sim–Est adjunction.
- VW-2009-Bayes — Bayes nets for currency unions and trade; international monetary link before MoMaT-I’s currency-area topoi.
- VW-1996-Mamba — shortfall risk measurement; early risk-buffer thinking echoed in MoMaT’s ABZ hierarchy.
Essays
VW-2006-WiWo — From Film Producer to Economist (2006)
Interview by Jan Mallien (Wirtschaftswoche). pdf
Early public statement of the same program: economics needs a formal language for intentional agents, not physics-style differential equations; category theory as translation between mathematical formalisms; the Mannheim lone-fighter phase before the collaboration with logicians and computer scientists that became MoMaT.
VW-2013-Studia — Logical Simulation of Economic Phenomena (2013)
Interview with Andrew Schumann (Studia Humana 2:1). pdf
What I said in 2013
Economics needs a higher-level language than functional analysis alone: types, units, logic, composition of argument lines, reflexivity (Lucas, Soros, endogenous institutions). Coalgebras as a functorial interface for games and belief hierarchies; category theory for local-to-global transitions; money as the language of the economy and a categorical dual accounting; the ambition to program the economist — theory as runnable code (Haskell, corecursion). Vision of a self-organized SAP for finance ministries, theorem proving as type transformation, and global solutions (algebraic geometry, cohomology) instead of static equilibrium prose. Diagnosis of Euro-era “holes” where macro dynamics and national double-entry bookkeeping do not close.
Then and now
| Keyword | Then (2013) | Today |
|---|---|---|
| Mathematical level | Functional analysis, Fortran; gap between natural language and formalism | AccCat / DecCat / GovCat |
| Composition | Theory lines not composable; meta/object language clash | Open Games, OiC-Engine |
| Reflexivity | Lucas critique, Soros as corecursion, endogenous theory | Topos, DecCat do-see |
| Theory is code | Lisp/Prolog, Haskell corecursion; meta-interpreters | OiC.OS, OiC-DSL |
| Money / bookkeeping | “Language of the economy is money”; categorical double entry | DEB/QEB, gauge invariance |
| Local → global | Sheaves, cohomology, glueing; AG for macro | Sheaf-Topos, MoMaT-I |
| Meso layers | Critique of pure econophysics | ABZ hierarchy, LiquiPool |
| Macro holes | Euro “holes”; Betti numbers as metaphor | Homology, constructive closing |
| State software | SAP for finance ministers; proof engine | Engine + Agda GovCat (partial) |
| Edgeworth / AG | Edgeworth box as algebraic geometry | still vision |
Today — in the program
AccCat / DecCat / GovCat — MoMaT-A replaces ad hoc DSGE layers with three categories on one site: bookings (AccCat), compositional decisions (DecCat), contracts and compliance (GovCat). Lawvere theories T_DEB, T_Val, T_QEB supply the types and units that were missing in the household lecture.
Open Games, OiC-Engine — Compositionality that seemed impossible in 2013 is the main line from VW-2018-CGT through string diagrams to the engine canvas: models plug together like code, not like isolated equilibria.
Topos, DecCat do-see — Reflexivity is not Soros alone but adjunctions and internal logic: agents that anticipate policy live in DecCat forward/backward ports; the Lucas critique is answered by sheaf semantics and topos-internal truth, not exogenous shocks.
OiC.OS, OiC-DSL — “Program the economist” became runnable institutional software: .oic files, trace/explain — mathematics written down as running software, not metaphor.
DEB/QEB, gauge invariance — Generalized double accounting: quadruple entry via profunctors, unit of account as unit of adjunction, Pacioli invariants — the 2013 phrase “categorical dual accounting” in monograph form.
Sheaf-Topos, MoMaT-I — Local-to-global via Grothendieck sites and glueing (Nostro/Loro, Außenbuchhaltung); MoMaT-I adds the Ouroboros deployment ladder and currency-area topoi instead of classical GET algebraic geometry.
ABZ hierarchy, LiquiPool — Meso structures between micro and macro: banks, supply chains, ERP; MW-2025-SCF shows bilateral MoMaT with Shapley clearing — composition beats addition.
Homology, constructive closing — Macro “holes” are not metaphors only: research line treats H¹ ≠ 0 as liquidity gaps; MoMaT closes books constructively rather than patching dynamics onto inconsistent national accounts.
Engine + Agda GovCat (partial) — The 2013 “SAP for states” exists as engine and GovCat machine-checking in Agda, but not yet as a finance-ministry workflow product; contract/constitution generator on button press remains open.
Still vision — Edgeworth box as algebraic-geometric information of the contract curve; fully automated OCA/constitution typology — named in 2013, not yet built.